The frame should be treated like any other piece of wood; either the BORACARE or the JECTA GEL would do a good job of taking care of problem. If it's a small frame, you could opt to use an INSECT STRIP to essentially fumigate the piece whenever sawdust appears. This is very easy to do and effective though not "permanent". It's good for small wood pieces such as wood models, decorative statues and items which are difficult to treat with either Boracare or Jecta Gel.

Basically all you do is take the piece and place it in a zip lock plastic bag that you can make "air tight". Large kitchen or 55 gallon sized bags will work too. Next, you set the Insect Strip in with the piece, seal it up real tight and leave it for 1 week. Insect Strips are used for closets and other small confined areas where they slowly release killing moths and flies. When used in a small air tight area like this they'll work on any kind of wood beetle too. Again, the treatment won't be permanent but it will get larvae and active adults. And in most cases, after 1-2 treatments like this the problem will run it's course and be done. After a week the piece can be removed and placed back out as desired. You can then seal up the Insect Strip to save it should new activity be found. If new activity is found, repeat the process. Since the cycle of these beetles can include long delays between active stages of either larvae or adults, you might have to do a few treatments before complete control is achieved.

One thing is for sure: If the infestation is active, no doubt more beetles will emerge.

And powder post beetles only eat wood so the fabric is not at risk directly from the insects.

Lastly, there is always the risk that any piece of furniture or part of the structure that demonstrates an active powder post beetle problem can lead to other items made of wood getting infested too.

Treat as explained in our POWDERPOST BEETLE CONTROL article. The section on furniture treatments applies to this picture frame.

Here are direct links to the information and products listed above:

Boracare:  http://www.bugspray.com/catalog/products/page52.html

Jecta Gel:  http://www.bugspray.com/catalog/products/page156.html

Insect Strips:  http://www.bugspray.com/catalog/products/page307.html

Powder Post Beetle Control Article:  http://www.powderpostbeetles.com/powderpost-beetle-control#furniture_beetle_treatments