If there's really no possible way to fix it then yes, a tarp which is properly added willhelp protect from any further water damage. Simply stapling it isn't sufficient for more than a day or two: winds will either pull the staples loose or tear the tarp, or both. The best way would be to get a tarp which is much larger than you need and some 2x4s. In the places where you are affixing the tarp to the structure, wrap the end of the tarp around the 2x4 a couple of times, and then nail or screw through the 2x4 into the structure. Make sure you get into some solid wood (a joist or stud) instead of just the sheathing.
In your situation (older, not financially or otherwise able to fix it properly) I would reach out to family and friends, and/or check with local government. Someone should be willing to help you out, or maybe there is a local non-profit who can help.