It takes a few days after food is exhausted for the peeps to get hungry, and then they start starving to death one per day. Your peeps eat one fruit or vegetable each day, so for two days your peeps will eat vegetables. After that they'll be out of food, and start to get hungry, but you won't start losing peeps right away. After 5 more days my guess is that you would lose at most one or two peeps, and possibly none.

During that time, weeds and trash will accumulate, and when your beauty meter drops enough, peeps will move out.

You will not lose more than one peep per day. I think that means from any reason, but I don't know, so for a worst case scenario, you might lose one from starving and one from moving out. I don't think you can lose all your peeps even if you leave for a month, but again I'm not sure (and all those skeletons in my VV game might suggest otherwise).

Plant fruit trees. Fruit trees bear 3 fruits every 3 days or so, and don't need to be replanted. Even though peeps will survive even if they eat only every third day, what I do is to plant 3 fruit trees every day early in the game until I have 9 trees. Since they bear fruit on a schedule, that means 9 fruits will drop every day forever.

My bet is that just three trees (9 fruits every 3 days) would prevent starvation, but by staggering planting I am hoping for 9 fruits every day. I assume that the same peep wouldn't miss out on getting a fruit every day, so nobody would starve.

I also keep about 60 vegetables planted, but that's just overkill.

As for the trash in town, I activated the town cleanup ordinance but the townies are still pretty lazy. If I had two identical devices I would set up two situations, both with lots of fruit tress and one with and one without that ordinance, and then leave them alone and see what happens. Unfortunately, I don't have the hardware to test that.

Seven fruit trees will give you 21 fruits every 3 days. Since fallen fruit disappears at the end of the day, it would be best if they were planted on different days. For instance, if you planted 3 trees on one day, and 4 the next, after the trees mature you would get 9 fruits on day 1, 12 on day 2, none on day 3 (which is survivable), and 9 again on day 4, 12 on day 5, etc. I don't believe peeps will starve to death with only 2 days of hunger, so even if you planted just 4 trees on one day, it should be enough.

I think it is a random pick who moves out, but the last time I lost a peep it was the last one who moved in. That wasn't by starvation. I didn't keep an eye on the beauty of the town. Ooops. I tried to starve my peeps back in December and I don't think they died off in the reverse order of moving in. I am not at all sure, though.

I've wondered if a player could rid themselves of an annoying peep by stockpiling fruit and vegetables (peeps can't get to it in your inventory/storage), cutting down all fruit trees and harvesting all vegetables, then hand feeding everyone but the peep you dislike until the disliked one starves. It would take a while and feel kind of terrible.