Personal property protection is one most important benefits of having renters insurance. The policy does not usually cover items which wear out or break through normal use, but it will pay to repair or replace items which are lost, stolen, or damaged by someone other than the people covered under the policy.
Since any item in your possession is considered to be your personal property, such coverage includes borrowed and rented items as well as the things you own. For example, if you borrowed a computer from a friend it got stolen, your renters insurance would cover the replacement up to the limits on the policy. If you have full replacement value coverage, it will pay to replace the borrowed items regardless of their age, but if you have actual cash value coverage, it will only pay the depreciated value of the items.
Your renters insurance will protect borrowed items when you are away from home, as well. If you were to borrow a bike from someone and it got stolen while you went inside a store, your renter's policy would pay for the bike, or the depreciated value of it. The issue is going to be what your personal property limits are set to, and whether it is even worth filing a claim after the deductible is met.
The big concern for using your renters insurance to cover borrowed items is more a matter of protecting your insurance "reputation" than with the coverage itself. If the item only costs a little more than the deductible, it would be best to pay out of pocket. Similarly, if you already filed one or claims for loss or damages on any insurance policy in the past few years, filing another claim could be the trigger which causes your insurance rates to go up on all of your liability policies. One of the best ways to keep your rates low is to keep your claims to a minimum. Read other ways to get cheaper renters insurance.