I don't know about later reattaching, but the fragments left after a painting is cut out of a frame are saved to confirm authenticity should the painting be found. Rewards for stolen paintings encourage forgeries. If brushstroke, etc don't line up with the remainder it's easy to confirm forgery.

Source is Edward Dolnick's book The Rescue Artist about Charley Hill, a former Scotland Yard detective that was assigned to art recovery cases.

The Mona Lisa is painted on poplar wood, not canvas. It's shrunk a few centimetres since it was painted, but not because it was cut out of its frame.

The Isabella Stewart Gardner Museum in Boston had several paintings stolen in 1990. Due to a quirk in the Museum's charter, the empty frames with bits of painting are still on display. Here are some pictures.

Followup question: do art thieves really cut paintings out of their frames? I've seen it in movies of course, but have no idea whether it's just a film trope.

From an Art Conservation point of view, those pieces of canvas would indeed be preserved and when/if the painting is recovered, they would be reattached and the "seams" would be reinforced. A conservator will always strive to preserve as much of the original work of art as possible.

To simplify the process a bit: a clean cut to the canvas wouldn't pose much of a problem if the canvas is in good shape (which it would most likely be if it's in a museum), so "stitching" the pieces together is the easiest solution. After that, conservators could perform other types of operation to repair any damage the painting might have suffered.

Sources: I can't think of any texts that deal with this particular scenario, but my answer is based on experience and conservation theory works such as Cesare Brandi's Teoria del Restauro and Umberto Baldini's Teoria del Restauro e unità di metodologia, which explain the importance of preserving as much of the original materials as possible.

The real question is why don't they also steal the frame? Framing is expensive damn it!

While I understand you're asking a hypothetical question, you need to understand that this is such a rare circumstance that many of the answers are speculative.

Three things to keep in mind:

• Art theft is very rare - its much more common to see it in TV/movies than in real life.

• When artwork IS stolen its often kept whole (Nazi Europe) or entirely destroyed (Palmyra).

• In the rare cases that paintings are cut out, they are not always returned.

The best examples of what you're asking is the Isabella Stewart Garner collection.

Theoretically, the painting could be re-attched. When a canvas rips, the pieces can be sewn back together. For an entire canvas though, it would probably not be done.

I'd buy the fragments. I think it's more interesting that the painting was stolen than the actual painting.

It's a historic relic