It is as simple as you just described - assignee contacts sellers and says, “I’m pinch-hitting.” Generally, it is a good idea for the original buyer to let the seller know about the assignment in advance so there are no surprises.
This may be a silly question, but I figured unless asked it’ll remain unanswered.
If I get a house under contract at 59% LTV and use “and/or assigns” next to my name, then I find a fellow investor who wants to buy it at 65% LTV, do I have to notify the seller that he will close with someone else? In other words, what needs to happen to keep things clean after my buyers pays me the difference for the contract assignment?