This is classic offer and acceptance in contract law. If you did indeed offer, in writing, $50k for that person's house in something that wasn't a joke offer, and then other person accepted for whatever reason before you rescinded the offer, that's a valid contract for sale of something. There may be additional concerns given it's real property and not goods, but the point stands: the owner was presented with an offer, then countered the offer with $50k, and the first party accepted the offer. All in writing. This creates a valid contract.
Indeed, however an offer by itself doesn't create anything binding. One of the other critical pieces is the acceptance of that offer. Otherwise we'd have situations where someone was forced to sell their house simply for being in the presence of an offer!
