NapaJohn

Thanks, Macybaby. You're correct that there are some cabinets that would accommodate free arm machines, but I assumed the OP referred to cabinets like the Queen Anne Cab or the #42 as those are the type I think of when someone mentions Singer cabinets. I also image googled a Morse 300 which appears to be a 15 clone but I probably shouldn't have assumed. (I know what happens to u and me!) It's entirely possible she's using the Morse in a case bottom or just set in a free arm cabinet. I've also seen a Singer Athena 2000 in a cabinet that I thought the cabinet would probably work with a Pfaff, but didn't buy or try it.

Nice set-up with your Viking. My mother has a similar set-up with her newer (than mine) Pfaff which has a formica insert my stepfather made her but it sits flush with the cabinet and you also have to remove the insert to change bobbins.

I have the cabinet my father purchased for my mother (along with the Pfaff 332-260) in 1957, although I don't think it's actually a Pfaff cabinet, it does work. There is actually an L-shaped insert that uses a tongue and groove joint that slides in the front of the machine which would probably work for some type of Singer but it won't work with the Pfaff. Here's a picture of a Pfaff 332 (my most recent acquisition) in the cabinet:

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Here's a picture of the back:
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I'm not sure if you can tell from this pic but the bed extension is slightly above the cabinet top. Since the bed is rounded at the edge, it has never been a problem. I have attempted to put an Elna 62C and a Singer 500 in this cab but they are both a little too short and had to place them on pieces of wood to get the proper height. I thought I would make a plexi insert for around the bed of the 62C but that's not high on my priority list.

The bed of this cabinet does have holes in it to attach a machine (but I'm not sure what machine they are designed for) and there are two dowel-like "levers" you slide to drop the bed down to store the machine. I never drop it with the Pfaff as I never thought it would be easily secured. Here is a pic of the bed dropped.
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Finally, here is a pic for ChattyKathy. When you go to look at the Pfaff, pop the top off (it easily lifts off with no screwdriver required) and check to see if the belts are in good shape.
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The double belt on the left is the timing belt and if it's missing or mushy then you'll probably never find a way to replace it. The belt on the right is the motor belt and you might or might not find one of those. They are cotton or nylon with metal cleats and be very careful when cleaning your machine not to get any oil or liquid on them as that will hasten their demise.

The other thing to check on the 360 is the electric plug on the back of the machine. Some of the plugs are broken and I think the 360 has sort of a double prong plug that has been described as "unobtainium" if it's not in good shape. The 332 has a regular plug on the back and still available. I've actually used a Kirby vacuum cleaner cord on my 332-260 for years as an OSMG told me they were easier to get and cheaper at the time. One benefit is that with a cord that long, I can set it up anywhere and still reach an outlet!

I would definitely check out the cabinet, though. Many of the original Pfaff cabinets are really really nice and I would probably trade a couple of other cabinets to have one!

Good luck!