Inheritance FAQ once stated that when you bought a card, it became yours for Inherited when-buy abilities to work. the errata last year displaced those any more, is the ruling still valid?
If yes, then interaction with Market Square is problematic now. MS usually can’t react to trashing from Supply (e.g. Salt the Earth), but if you buy a card (just yours though it’s still staying in Supply) and trash it from there in the buy window — I mean during resolving when-buy for it — you can activate MS. There is a sample: Buy an Inherited Estate with a Haggler in play, gain a Ferry-ed Lurker, Innovation it to trash the Estate.
I assume the FAQ is not specific to Estate but deduction from general rule, so not only Inherited Estate but all bought cards are yours on buy, which can refine the above example using more Events than recommended. I’m not sure whether the assumption is right, though.
your cards are defined by 2nd Base rulebook and by some posts in the forum, and relevant part of Inheritance FAQ is:
An Estate is yours if either it started in your deck, or you gained it or bought it, ...
(The rulebook of Adventures, 2nd, p. 12)