Some relatives of mine have low blood sugar. Doctor told them to eat table sugar whenever they get a feel of low blood sugar.
AFAIK table sugar is not good for health.
What are the natural and healthy ways to increase blood sugar?
There seems to be some misunderstanding here, so this is going to be a long answer.
Our body is very, very good at regulating several physical and chemical parameters inside itself 1. he most well known is the temperature: it does not matter if the air temperature is -50 Celsius or +50 Celsius, it will do its best to keep you between 36.5 and 37 Celsius, and will mostly succeed at that, with amazing precision, unless you get exposed for a long time to temperatures which are either too hot or too cold for its capabilities to adapt.
The system for regulating blood sugar is similarly complicated. The body is actively trying to keep the blood sugar at a level which it "believes" is best for it, and unless its regulation mechanism is badly broken, it's succeeding at that, at least in the long term. Short term upward spikes and downward spikes do happen in the healthy human, if you are either eating or using up sugar at a rate too quick for the body to compensate.
There is a theory that eating too much glucose and other simple sugars can break this regulation system. The reason: they cause upward spikes when they are eaten, because they can be transformed into blood sugar very quickly, quicker than the body can stabilize the level of blood sugar. The body then goes into "alarm! too high blood sugar!" mode, and mobilizes whatever it can to reduce the blood sugar before it causes problems. That overreaction gets the spike down soon, but the high hormone levels stay, such that you now get a downward spike in blood sugar.
The supporters of the "this is unhealthy" side of the debate (note that the matter is not yet settled in the scientific community, although I'm under the impression that it has been gaining ground lately) say that first, this creates hunger pangs (because when your blood sugar falls, one of the body's mechanisms to get it back up is to create the feeling of hunger, so you supply it with more food) and leads to overeating, and second, frequently straining the blood sugar regulation system will make it less effective over time, because it's overworked, and also because the body gets less sensitive to its signals. This leads to metabolic syndrome and later, diabetes type 2, such that the body can no longer keep the blood sugar at the level it wants it to be.
The gist of it is: The reason why table sugar is considered unhealthy is that eating it raises blood sugar. Consequently, any other food which raises the blood sugar is just as healthy/unhealthy as table sugar.
Now you can say that your friend seems to need her blood sugar raised, so for her, eating a food which raises it is not unhealthy. This is indeed logical, but in that case, then sugar is not unhealthy for her either. If she wants to try to raise her blood sugar with food, then pure glucose is indeed the best she can do, followed closely by table sugar.
That being said, if I were her, I would not try messing with my blood sugar levels through food. Her sugar regulating system is either working well, or malfunctioning. If it is working well, then there is nothing she should be doing about it, despite it not fitting some norm. If it is malfunctioning, then she must have some serious underlying condition, and she should seek diagnosis and treatment for it instead of eating sugar (which is unlikely to help for timeframes over several minutes to an hour anyway). If she mistrusts her general physician's competence in that matter, she should visit an endocrinologist. If she has no symptoms from the low blood sugar and trusts him that there is no cause to worry, she should keep everything as it is, instead of trying to override her hormones by gorging on glucose, or any other food which raises the blood sugar level.
There are two cases that I know of where she can have too low blood sugar measured besides this value being the right one for her or her having a hormonal disturbance/diabetes. First, if she exercises too much, or after too long a time without eating (or drinking sweetened drinks), she can cause a downward spike in an otherwise healthy body. It will go away soon by itself. Second, if she is on a ketogenic diet (only fat and proteins, no carbohydrates at all), her blood sugar will plummet permanently. The solution there is to go back to normal food - unless there is medical indication for the ketogenic diet, such as epilepsy, in which case a health professional should decide whether the side effects are worth continuing it.