I have been working for a couple of days on a painting with an old tear. As well as having broken canvas fibres the surrounding area is distorted where the fibres have stretched before breaking. In the past someone has put on a thick paper and canvas patch to support the tear, which I’ve taken off. I’m always wary of old repairs after the time I had to remove someone’s attempt that consisted of an old crossword and lots of PVA glue. Luckily, this one hasn’t been so bad.
For a small tear it is usually possible to bond the broken threads before adhering a lightweight patch to give further support to the torn area. If the tear is larger it may be necessary to support the whole canvas with another piece of fabric, in a process called lining. Sometimes it isn’t possible to bring the broken threads together so I have to cut a new piece of canvas to insert into the gap. Of course, I try to keep my repairs reversible, in case they start to fail at some point in the (hopefully distant) future, by choosing suitable adhesives and documenting my treatments.