All I know is you have a set that fits an open arm machine, not a flat bed machine. And that the feed dog inset is more square in shape compared to the one that is long and narrow.
The yellow box would have held the chain stitch attachment parts, which is the needle plate and then a round part that slips into the bobbin case.
My husband picked up the monogrammer for $2, just to see if the cams would work with the other unit. At the time I didn't know much about them and did not realize it was for an open arm machine.
For fun I was looking on eBay - there are many to choose from. Watch though because Kenmore often lists the models as the last digits of the machine, you have to make sure the first digits are in the 158 series. I've seen some that were from 13XX up to 19xx that your items should fit, so then you need to decide what features you want.
From looking, I think the numbers are not necessarily indicative of age, meaning a 13XX may not be an older machine than a 15XX machine. It seems more like those may indicate features, such as a group of machines may have been 1312, 1412 and 1812 for the age group. I was looking for a machine with specific features and ended up with a 1833. This one has the ability to do stretch stitches, so it is one of the later models with two cam followers, earlier ones only have one cam follower. Kenmore called this feature "verigator"
Right now on eBay, there is a model 134x, 154x and 194x, all are open arms and all look like your attachment will fit. But I also found a nice 162X machine- main thing is it's an open arm. And if you want one that chain stitches, the needle plate has to have the smaller square removable insert that goes around the feed dogs. Some models have a solid plate so you can't use the chain stitch adapter with them.
The full model number will be on plate on the underside of the machine, and it will be 158-MMMMx (five digit) but the "model" number listed on the manual will only be the first four of those digits.