To remain stable

You MUST give a sentence to figure out a word's FUNCTION.

For example:
He had difficulty in getting the horse to remain stable.

I want you to remain stable.

It is difficult to remain stable at exam time.

WHAT'S YOUR SENTENCE?

It's a standard construction:

to remain calm
to get excited
to remain hopeful
to get lucky
to remain stable

I don't see the problem.

It' not a problem.

It's just unfair to be given a phrase or word and be asked what is means or what is its function, especially in English. By asking for context, it makes the question more clear.

This "linking verb" (remain) is somewhat of an exception and needs to have more explanation.

As Collins English Dictionary explains it, "copulas [linking verbs - me] may serve to link... adjectival complements, as in sugar tastes sweet..."