If for example, I have a Prolog predicate like a(A, B).
Is it possible to collect, given a value of A, is it possible to collect all values of B that succeeds the predicate a, into a list, without using built in predicates such as bagof/3 or findall/3.
You have two obvious options (obvious to me; it seems there is more). One is to indeed use the database to save the state. This has at least one pitfall: depending on the name you decide to use for the temporary state, you might destroy some other state your program is keeping. This is the same old "global state"/"global variable" problem that all languages suffer from.
The other option would be to use a "local variable" and non-backtracking assignment to it to keep the temporary state. This is most probably going to be implementation dependent. For starters, you can look at nb_setarg/3 for SWI-Prolog.
However, both solutions are silly, given that you have findall, bagof, setof. You must motivate the need for something else to replace those. Just saying "is it possible" is not good enough since it is possible, but completely unnecessary, unless you know something else that you aren't telling us.