I sort of kind of did this.
Our mortgage rate was a bit high (5.85, I think?) and we couldn't refi because we moved overseas so it was no longer owner occupied. I mentioned this to my parents in passing, just venting my frustration. A few weeks later, my dad offered to lend us the money to pay off our mortgage. We'd borrowed from them before for our first mortgage, and it had worked well, so that wasn't a concern. However, our mortgage balance was slightly more than dad wanted to liquidate. We had a HELOC that well more than covered the difference, so we pulled out money from that to make up the difference. At that point, we had no traditional mortgage, just them money we owed my parents, and the HELOC balance. In addition to paying my parents every month (with a set interest rate and an official lien on the property), we've aggressively paid off the HELOC balance. It is a variable rate. I think it was 2.6 and went up about 6-8 months ago to 2.85. Still an amazing rate! And it can't go up more than 1% per year, so there will be no ugly jumps. Even though it was interest-only, we made it a priority to pay it off quickly. We started with about $60k on it 19 months ago, and we are down to $3k today.
As I said, we weren't too worried about the interest rate because it was so low that it would have had to go up a lot before this stopped being a good deal, and because it is limited to 1% increase per year. We knew we had the cash flow to knock it out pretty quickly. We will beat our goal, which was 3 years but we'll have done all $60k in less than 2 years. I'm not a huge numbers person like so many here so I haven't bothered running the numbers, but I know we've saved a ton or money, going from 5.85 to 2.6/2.85, and also because that allowed us to refi the rest at a lower rate (though higher than 2.6!) and in to a shorter term, which we wouldn't have been able to do without a way to make up the difference in what my parents were interested in loaning us. Had it not been a dollar amount we felt very, very confident we'd be able to pay off pretty quickly, the risk of that variable rate would probably have been too much. But for those with smaller mortgages and/or very high incomes-- allowing them to pay off the HELOC quickly-- and those who have a HELOC that has limitations on interest increases, the risk is fairly mitigated and I think it can make sense. IOW, I think it would be too risky if it was going to take 20 or 10 or even 7-8 years to pay off or if the rate could risk quickly, but for >5 years and with a limit to the increase, there was very, very little risk as at 1% per year, it would have taken 3 years just to get almost up to what we were paying on the regular mortgage. (And that doesn't take in to account the fact that over those 3 years, we'd have paid off a ton of principle and would still have been paying less in dollars even at the same interest rate.)