What is the safest way to unload a timeshare right now?
Depends on what you have. Is it paid off? If its not I doubt you can unload it. It would need to be paid off. Most timeshares are given away for free on eBay and even right here on TUG.
They all have no loan....
If it paid off list for free on the timeshares for free section of this site
You could try to list for some minimal amount in the marketplace but minimal is key.
You can offer to pay closing and transfer to make it more appealing than others
If it not paid off you can either keep it, or if thats not an option take stop paying and take the hit on your credit
What's not safe is paying a company to list, cancel or sell your timeshare. They all just get you to stop paying anyways, and if you get foreclosed on, they consider their job done. Same results as just stopping payment on your own except now you are out whatever you paid.