You can expect the inner core stem to develop into one or more usable scallions and over time form another bulb(s). However, the tendency is for the tuber to begin rotting and the bulb formed is usually woody in texture and strong flavored.

Anything I can do to prevent it from rotting? Water sparingly?

Water is usually involved but the rotting begins in the onion meat as it shrivels.

I can't tell you that this will work the way you would like but aside from the decaying bulb, onions are very transplant hardy plants. I would pull the plant at the point when the bulb softens and remove the outer bulb, being careful to maintain the core thru the rootmass. Then replant that core.

You can do a few seemingly drastic steps of pruming both the excess roots and the green growing top from the plant without harming the plant. You would only take these steps if you wanted to but I shear roots (once at transplanting)and tops (2-3 times during seedling growth leaving 2-3" of green top) on seedling plants to make transplanting of a stockier stemmed seedling easier.

I just mention this so that you won't hesitate to lop the top ~6" off you plant and dice it up in your salad. The plant should just send up more growth from the center core each time.

The other possibility is that it will send up a hollow stalk and, if it gets enough light, will flower. And then die.
Planting scallions will generally get you either an onion or more scallions. Planting an onion generally doesn't get you another onion - just a flower (and not a very exciting one).
Try this question on the allium forum.