There's no such thing as a "gift of equity". If your mom paid $40K for the house, it was worth $400K and she sold it for $300K, then she has a taxable gain of $260K. Period. End of story.
The buyer purchased the house for $300K and it has a value of $400K giving the buyer an instant $100K of equity. The seller didn't "GIVE" anything what-so-ever. The seller just sold it for less than it was worth. That's it. The buyer's cost basis on the house is $300K, exactly what they paid for it.
