Alas, you cannot protect yourself from these toxic substances once they are in your body. Further, as currently phrased this question is awfully broad. We have managed to produce a gigantic amount of different harmful substances and covering them all in this answer is really not possible. Instead this answer tries to generalise about fat-soluble and long term stable materials that get liberated in weight loss. Any substance mentioned in citations is meant as one example, most examples do not generate generally applicable advice.
There are some options to consider to protect you from the harm these substances do. For obvious ethical reasons most of the following is based on experimental data in vivo and not nearly enough on human trials.
The good news is, these substances are generally very stable, but not indestructible. They do accumulate in fatty tissues and are hardly excreted or broken down. But eventually some of them are broken down or just excreted.
The fate of inhaled (14)C-labeled PCB11 and its metabolites in vivo:
This study shows that PCB11 is completely absorbed after inhalation exposure and is rapidly eliminated from most tissues. Phase II metabolites dominated with a slower elimination rate than the PCB11 or phase I metabolites and thus can best serve as urine biomarkers of exposure.
The dynamics of POP release and damage are still investigated and indeed worrisome:
Dynamics of persistent organic pollutants in obese adolescents during weight loss:
In general, POP levels raised by 1–3.5% per kilogram weight loss. The increase in the POPs levels during weight loss did not affect the profile, which remained similar over time. Weight reduction is recommended for overweight and obese individuals in order to decrease the risk of weight-related health problems. However, the results of the present study indicate that the increase in the levels of POPs released in blood during weight loss might be of concern since literature suggested that they can be associated with endocrine disturbances. The clinical significance of the weight loss induced serum pollutants levels observed in the present study is, however, as yet unknown. Beneficial health effects of weight loss are generally expected, however, the increase in the internal exposure may adversely act on health since metabolism and/or elimination of POPs may be altered in adolescents as compared to adults. Further studies are therefore needed to address this issue.
To minimise the damage they will do there are a few routes open, all of them weak and some of them based on preliminary results and reasonable speculation:
Slow down their release
Although it was already priced into the original question, the slower the weight loss the slower the release of persisten organic pollutants (POPs). The dosage makes the poison and therfore slowing the release of these unwanted materials is all the better.
Increase excretion and elimination
As should be obvious highly lipophilic substances like those in question are not easily deposed of. But the body does eliminate them, very slowly, once they are mobilised from the fatty tissues.
That means drinking a lot helps, sweating a lot helps and loosing blood helps. Speeding up the metabolism, exercising or even going to a sauna seem quite beneficial.
The loosing blood needs special mention since it would be unethical to go donating blood if anyone does it to get rid of toxic substances. Yet it seems strange to advise blood-letting again, even when this involves a round of the venerable Hirudo medicinalis treatment. But once the substances are mobilised they are transported via blood to areas you want to to avoid them ending up. Extracting this contaminated blood is not the strangest of ideas then.
Human Excretion of Polybrominated Diphenyl Ether Flame Retardants: Blood, Urine, and Sweat Study:
Conclusion. Blood testing provides only a partial understanding of human PBDE bioaccumulation; testing of both blood and perspiration provides a better understanding. This study provides important baseline evidence for regular induced perspiration as a potential means for therapeutic PBDE elimination.
Finally, the infamous Olestra and its kind may have a role of value:
Non-dioxin-like Polychlorinated Biphenyls (PCBs) and Chlordecone Release from Adipose Tissue to Blood in Response to Body Fat Mobilization in Ewe (Ovis aries):
To be efficient in depurating animals, undernutrition should be combined with a strategy increasing the fecal lipid output and consequently the POP excretion pool, such as the supplementation of the diet with nonabsorbable lipids. This combined strategy was tested with success for hastening the removal of PCBs in chickens. Further studies are needed to assess its efficiency in larger animals such as ruminants, where only nonabsorbable lipid supplementation in well-fed growing lambs or lactating cows and goats was tested. With regard to CLD, which accumulates in the liver rather than in AT, undernutrition seems not to represent a valuable strategy because of its probable deleterious effect on liver size and metabolic activity.
Limit the damage the substances can do
There were a few theories proposed for certain mechanisms of action for these substances, one of them being endocrinal disrupters another being promoter of oxidative stress.
Especially the latter has received some attention and the old adage of food being your medicine came to life again.
While "eat healthy" seems like a no-brainer on this front it is currently the best practical advice available. These findings are very limited by their nature. Popular "anti-oxidants" have usually a very low bioavailability and even in those experimental settings used to study them in regard to POPs with scaffolding mechanisms their effectiveness was greater than zero, but still not very great.
Curcumin, resveratrol, CoQ10, NAC and just about all of the usual suspects for such a scenario showed some promise.
The environmental pollutant, polychlorinated biphenyls,
and cardiovascular disease: a potential target for antioxidant nanotherapeutics:
A final consideration to be made in the use of antioxidant therapies is that of the route of administration. Given their size and use, most studies have focused upon i.v. injection of nanocarrier systems. Yet, such intervention strategies are likely to be limited to acute and subacute exposures, as prolonged i.v. administration is highly undesirable. As such, exploration of alternative delivery methods, includ- ing inhalation, intratracheal, intraperitoneal, and topical administration, is needed. All of these methods have been tried for the delivery of antioxidant in free form. Clinical trials employing oral delivery of antioxidants such as curcumin in free form have been conducted several times, with variable dosage towards suppression of oxidative stress-induced inflammation. […]
Chronic exposure of environmental pollutants remains a significant health concern. Even now, PCBs pose a contin- uous threat to the health and safety of our population. As a result, we need a wide array of tools and strategies to counteract these potential risks. While effective and healthful nutrition is likely to be a major player in our strategies to minimize health hazards, as seen by clinical trials of antioxidant interventions, it is unlikely that nutrition alone is enough to treat or prevent all PCB exposure-induced disorders. As such, strategies that can reduce body burden, enhance antioxidant delivery to target cells, and capture PCBs before entering the body can potentially be used to provide defense against PCB toxicity. Furthermore, we know from other treatments, such as NAC for acetamino- phen toxicity, where antioxidant therapy can be an effective antidote. In order to enhance antioxidant therapy, strategies for effectively delivering antioxidants, such as nanocarriers, are likely required. Further studies for ideal candidates will be needed to best assess which compounds will be most effective at countering the toxicity of co-planar and non-coplanar PCBs. Finally, while studies with injectable nanocarriers provide some promising results, such routes of administration are not likely acceptable for chronic delivery systems.
The best treatment is of course preventing any new harmful material from entering your system. For that it might be worth considering decrease animal fat consumption:
Plant consumption by grizzly bears reduces biomagnification of salmon-derived polychlorinated biphenyls, polybrominated diphenyl ethers, and organochlorine pesticides.