First, understand that I am not a tax professional, real estate professional, or banking professional by any stretch of the imagination. Additionally, all you've provided is a small snippet of whatever legal papers were completed by you in the bank, for this transaction.
Overall, it appears to me you have nothing to report on your tax return at all. The only thing you need to do is to show that the rental property and all assets were removed from service and disposed of by having "given it away", and that's it. You're done. There is no tax consequence on your 2019 return, one way or the other.
However, that doesn't mean there will not be a tax consequence in 2020 or a future tax year. All that snipped that you included in your post tells me, is that the lender has agreed to not go after you or your personal assets for collection of the mount you still owe on the loan, which I understand to be $379,000. In other words, the lender has "forgiven" that $379,000 and you don't have to repay it.
However, since you get to keep that borrowed money it's no longer borrowed money. It's "your" money now. (The fact you used it to buy a house with doesn't matter.) and you may have to pay taxes on that money. It just depends. Here's how this usually works on a voluntary foreclosure.
The bank will attempt to sell the property for the most they can sell it for. If they sell it for more than what you owed on it, then after the bank adds their fees to the amount you owe, if there's any money left over they are required by law to give that overage to you. It's also taxable income to you in the year they pay you that overage.
If the bank sells the property for less than what you owe on it, then the difference between what they sell it for and what you owe on it, is taxable income to you. If that happens, then in whatever year they sell the propery the lender will send you a 1099-C for the difference. You'll be required to report that 1099-C on your tax return and pay taxes on it. Since the property was not your primary residence at the time you elected the voluntary foreclosure, you will not qualify to be exempt from paying taxes on it under any forgiveness program.
So while the bank may have agreed in writing to not attempt any collection from you, it's a sure fire bet the IRS is going to get their cut any way you look at it.
