We are now inundated with the little fucks, and there are more and more of them. How do they survive without water and food?
They don’t. If there is an infestation they are getting food and water somewhere nearby. But a little bit goes a long way with roaches.
They can survive for some period of time with no food, some say a month or so, but they definitely can’t survive more than a few days without water. They can also happily survive eating cardboard and paper, glue, grease and oil, and other things we might not consider very nutritious.
In college bio lab, we had to dissect a cockroach. Evil, vile, disgusting, nasty… ANYWAY, roaches have quite a bit of fat covering their internal organs in the abdomen. I’m sure they utilize that fat to stay fed and hydrated for a LONG time.
Nasty, greasy, revolting, disgusting…
~VOW
I read they like the insulation in your TV.
They can live on virtually anything. Try boric acid, it does work. It’s messy but it works. I grew up in Florida so I know how hard it is to get rid of them. The thing about boric acid, is you have to let them run through it. You want to kill the bugs, but that does no good. They have to get it on them and take it back to the nest.
I also found boxes to be a plauge. If you order anything these days, don’t keep the box as it’s probably from a factory full of roaches. Or locker rooms too.
On the flip side, it could be bed bugs (and now I’m all itchy)
They also survive off each other’s carcasses.
They eat the glue used to hold cardboard boxes together. They also eat carpenter glue, and hide in upholstered furniture where they can snack on the glue in the wood at their leisure.
Nasty, ugly, disgusting…
~VOW
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I’d also heard that they can survive on their own carcass. Not just the stored fat, but that they reabsorb their own internal organs, starting with reproductive organs, when starved. I don’t have ta citation, this may have been a “fun facts” column from Highlight’s magazine as a kid.
Besides borax baits to kill the colony, seal up all cracks and holes. Based on the above posts, don’t use wood glue! 
Also, read this…