The thumb is sometimes required to play free strokes . After, it may be used to damp a previously played bass note or one that would ring sympathetically.
In my opinion, for what that's worth, it is just as mobile and agile as the fingers and is not kept fixed in place with weighted placement on a string. It might be touching a string very lightly to assist hand stability, but that job is sometimes fulfilled by one of the fingers and the thumb can hover above the strings, free to move agilely to the next bass note to be played. If your thumb is resting heavily on a string, you may have your hand balance too biased toward the thumb.
When the sun shines, bask.
Classical Guitar forever!