What happens to Worms you leave alive after destroying nearby Nests?

Worms cannot move - think of them as turrets but for the Aliens. Unless you eventually expand your base towards the Worms you left alive, they cannot do anything more to you. Worms are only created during enemy expansion according to the Factorio Wiki:

Worms are only created during enemy expansion when a certain evolution factor requirement is fulfilled

So leaving the Worms should be fine, but if you leave Biters and Spitters, they will go off and create new bases eventually, thus leaving any Biters and Spitters alive after destroying their base allows them to repopulate. It is probably difficult to do so though as Biters and Spitters will attack the player when you engage one of their nests, which essentially forces you to have to kill them or be killed. During the expansion process however, when the individual Biter/Spitter dies, it either turns into a new nest or a worm.

From the Factorio Wiki:

Every 4-60 minutes, a group of 5-20 biters/spitters will leave their base to create a new base which will consist of as many worms/nests as there are members in the group. This group will search for a suitable spot that's 3-7 chunks away from existing bases. The interval between enemy expansions is global, and the higher enemy evolution, the shorter the interval is on average. Furthermore, with higher evolution, the groups are bigger on average.

Once they have found a suitable spot, each biter/spitter in the group dies and forms a new nest or worm.