Nothing is assured.

The fraternity chapter should know how many men they need to "fill the house" (I'm guessing you mean "living-in") and plan accordingly before fraternity rush starts. Since a rushee can only accept one bid, at some point the fraternity chapter knows if they have the numbers they need. If they do not, then the fraternity chapter - like most IFC chapters - can continue to bid after "formal" rush is over. This would be similar to NPC's snap bids and COR/COB bids. Again, there is usually no total or quota for IFC so they may bid as many worthy men as they see fit.