What is the value of the house? This will help us asses the tax implications it more accurately.
But a few thoughts, If this is true and they are being offered a home for 10% of the market value. Their main goal right now needs to be how do they acquire this house. I'd want to see their kitchen blender, Pokemon cards, baby stroller and dads Xbox on craigslist right now.
You said they have the down payment money, I don't know how much they can afford but i always recommend a 30 year fixed. But in this case only, if a 30 year fixed is stretching them, i'd say get a 7 year interest only loan, or whatever loan gives them the most affordable payment. Since they will never be upside down on this house, they can always refi to a 30 fixed when they are a little more flush, or sell...
After they buy it yes, they can borrow more money from it, they have a ton of equity, banks like equity.
Tax implications on using equity, none its a loan, you don't pay taxes on loans.
Tax implications when they sell, only on the amount more than 500k profit. And if i ever sell a property where i make more than 500k, i'd happily hand deliver my check to the IRS in my new (ok lightly used) Bentley.
As for the gift tax mentioned, no idea. i know my grandparents inherited a home from their neighbor, they didn't pay a tax on it (and this home is in the heart of silicon valley). Is inheritance the same as a gift?