Always better to get it in advance
Yes, a buyer should be able to obtain title ins after the purchase, but unfortunately if there are defects in the title, the policy would contain exclusions and exceptions that may render the title policy useless. Since it is after the fact, it may be dificult to correct any deficiencies.
The warranty deed helps, however an imdemnification is only as good as the person giving it. . . . so if the Seller cant correct or has no assets to rectify the situation (if there is one) then the buyer may be out in the cold.
Part of the benefit of title ins is the search that occurs prior to the purchase so the buyer is informed before spending their money.
Contact a local title insurance company to see what they will do