Depends where the plant is.If outdoors, moisture may make your paper bag go a bit soggy, & stick to the seed head or pod, potentially harm the seeds & cause mildew or rotting. Or it may simply fall away and the seed is lost. I prefer something that will breathe a little , dry out quickly after rain and not suffocate the seed head.
Bits of cut-up old panty-hose, cheese-cloth, coffee-percolator liners. The first two can be re-used. Don't use anything to secure that will harm the stem or yourself, when you go to remove. A safety pin is fine if there are no children or pets around in case it falls. I use tiny craft-shop wooded pegs, can buy a bag of 100 for about $2 in Australia.
Depends on the size of the seed and the pod, too. For very large seed, mesh bags such as bulb /onion bags could work, for small seed like violas, you need something with no openings.

I have some Snow on the Mountain plants that I have been watching closely so I could collect the seed. Well I wasn't able to check them for about a week and this past Saturday morning I went outside checking out everything and noticed that the Snow on the Mountain seed pods had split open and all were laying on the ground. There was no mulch under those plants and the ground was very dry and without a lot of other debris. I'm sure I looked pretty stupid in my flower bed armed with my shopvac. It actually worked very well but I hope not to many people saw me.

Whatever works, Jim. I use my vacuum cleaner to get rid of bees nests on the porch. I've also cleaned out a couple of fire ant nests with it. I just drag the old Kirby out to the curb and fire it up. Those ants come pouring out of their hole and then they are goners. I add a little orange oil to the inside of the bag so they die and don't chew their way out. Course there are so many of them it takes a while, but the ones below don't know where their aunts went and they just keep coming. Anyway, I find a vacuum cleaner a very versitile garden tool.

Oh, yeah, little cotton cloth bags for seeds. They breathe, and they catch all the seeds. You can attach them with a little drawstring so you can reuse them. I got the idea from the Koreans who used cloth bags to protect fresh fruit on the tree branches from birds and bugs. Cheryl