Praise be to Allah.
The denture adhesive mentioned, and others like it, are usually used to hold complete dentures in place on the jaw, to stop them moving and to keep them steady when chewing and speaking.
The ruling on using a denture adhesive whilst fasting is based on knowing whether this adhesive will dissolve in the mouth or any of it will break off, or not.
Such things can only be found out by experience or by asking specialists.
When we asked some specialists in dental care, they told us that what usually happens is that this adhesive does not dissolve and nothing of it melts in the mouth or breaks off, because the way it is used is that it is placed inside the hollow of the dentures, then the denture is fixed with it on the jaw for which it was made.
The possibility of something breaking off from it only arises when removing the denture or if it moves from its place.
In that case, the pieces of this adhesive that break up will be in the mouth, and it will be possible to detect them, collect them in the mouth and then spit them out, without difficulty.
This is what is required with regard to food particles , or pieces that break off the siwaak and the like in the mouth.
With regard to the possibility of it dissolving, such that something of it could reach the throat and stomach without the fasting person realizing or having any control over it, that is not applicable in the case of this substance, because it is not like toothpaste, for example, which, if some remnants of it are left in the mouth, it is possible for it to dissolve and reach the throat and stomach.
It says in a statement of the Islamic Fiqh Council on the topic of things that break the fast in the field of medical treatment:
Firstly: The following things are not regarded as breaking the fast:
…6- Having a tooth drilled, or having a tooth extracted, or having the teeth cleaned, or using a siwaak or toothbrush, so long as one avoids swallowing anything that reaches the throat.
End quote from Majallat Majma‘ al-Fiqh al-Islami.
And Allah knows best.