I have an 15 year old bike and the crank bearings gave out due to lack
of grease. I cleaned everything up and replaced both. These are open
ball bearings in a light stamped cage. I greased the snot of them but
wonder how they hold it. There is no backside seal, backside as in
towards the center of the crank, and it would seem the grease would
just flow away.

I filled the whole area with grease but, is there a seal missing,
something to hold the grease in the bearings?

Two didn't fall out when the bearings crumbled in my hands, which
doesn't mean they shouldn't be there. Bearings did last 15 years
so ... so what :-) (The new stuff is all sealed up and comes as one
cartridge you just screw into the crank frame cylinder.)