A married couple buys a house together and only his name is on the records and he dies or they divorce will she get half of the house

Did this person have a will? Or is the wife the power of attorney for the husband? It may depend upon those factors. If the man has a will and wills the estate or certain items to someone, then the items should go to whomever is stated in the will to receive them upon death.

Now if it's a divorce... idk...

If they divorce, the divorce court will decide who owns it, also what state they live in can make a difference ( community property states,) also was home bought after they were married.

At the death, if there is no will, wife does have some rights to inherit ( are there kids? ) if there is a will, that can effect who gets it.