Welcome to JustAnswer, and thank you for your question.
Unfortunately as we age, our skin becomes very fragile due to losing the fat layer underneath the skin and some of the connective tissues. There isn't much you can do to improve that, except to make sure to keep your skin well moisturized. This will help a little to keep it from tearing.
Use a moisturizing body bath lotion rather than soap (Dove is a good one, but there are others), and a good moisturizing lotion right after bathing and once or twice a day. Pay special attention to the areas that are exposed the most.
Wearing garments that cover your arms helps, but may not be practical in the summer.
When you do injure yourself, you need to be very careful with the cleaning and treatment of the wound to speed healing and prevent infection. It's not good to leave these type of wounds open as they can become infected very easily. You will need to get some supplies to keep on hand. Ask the pharmacist at your local pharmacy to help you locate these items:
Sterile water or normal saline solution
Non-adherent bandages (like Telfa)
Gauze roll 3" of the "stretchy" gauze (like Kling)
Q tips (keep these in the original container to keep them as clean as possible)
When you tear the skin:
Never use tape on your skin. No bandaids, no tape of any kind. This will just pull more skin off.
Never use plain gauze on the wound, it will stick and when you try to remove it the skin will come with it.
Dilute the peroxide: 1/2 sterile water or saline, and 1/2 peroxide
Pour this over the wound, then rinse with plain water or saline.
If skin flaps have become displaced, use a Q-tip to very gently coax them back over the skin in a flat position.
Apply some of the antibiotic ointment to the nonadherent dressing (try not to hand the dressing too much, you don't want to put extra bacteria on it) and smear it around (can use another Q-tip to do this).
Apply this over the wound.
Use the stretchy gauze to wrap around your arm a few times to secure the dressing and to cushion it.
Tape the gauze in place, but do not let the tape touch your skin.
Repeat this only once per day until it is healed enough to leave the dressing off. If the dressing sticks a bit, use the peroxide/water mixture to wet it to loosen before trying to remove it. When the wound is either completely closed or solidly scabbed, you can leave the dressing off. Then just keep it clean and dry.