Take a look at the video on the site for Art's Gun Shop. It explains the process very well. Art's would be a good place to have it done if he works on the 101. There may be some cheaper, but none will be better.
The back 9 or 10 inches of the rib on my 101 SB came loose a couple of years ago. I remembered seeing a post here on TS.com about resoldering ribs on 101's and had saved the text of the original post. After some deliberation I decided to try it, figuring that I could always send it out to someone else if it didn't work.
Well, it apparently did work, as I've shot the gun two seasons and it's still holding together. Didn't have to reblue it either! Here's the details:
"I have resoldered many, many ribs that came loose, most of them Winchester 101's and maybe 4 Perazzi MX-8's It's quite easy and take about 15 minutes.
Get a 1/2" wide strip of 320 emery cloth and put it under the rib area where the solder broke loose. Clean that area on the barrel lightly. Blow out any debris, now take a toothpick any apply solder flux on top the barrel where you just cleaned.
Take a strip of lead solder on a flat surface and hit it with a hammer a few times to flatten it out to about .010 thick. Now Cut the flattened solder with scissors into 3/8" pieces and stick them every inch apart between the top of barrel under rib. Clamp lightly the barrel and rib with 2 C clamps making sure you have packing between the clamping surfaces so you don't mar the finish. You only need a few pounds of clamping force to do this.
Now fire up your map/propane torch and start moving the flame in the area where the rib and barrel meet and keep the flame moving in the working area, switching from one side to the other. Once you see the solder sweating out of the joint, remove the heat and let cool for 10 minutes. After removing the clamps, go over the area with 0000 steel wool and you'll never know it was repaired."
Just regular old rosin core solder from a spool that I've had since the 70's.
Not sure if the new, EPA approved solder being sold these days is the same tin/lead composition, so you may want to dig up some of the old stuff to try.
Soft solder is what Olin Kodensha (Winchester) and BC Miroku (Charles Daly and Browning) used. Took 'em awhile to get the hang of good solder joints, I guess, as popped ribs were fairly common back in the early days for both of those Japanese manufacturers. Oddly, SKB never seemed to have any troubles.
Silver solder would be great for a complete teardown and resolder, but I wouldn't try it.