Several years ago, my then boyfriend, now husband, was assigned to some travel for work and lost track of his cherry tomatoes. The remaining tomatoes fell off the vine and the next year he thinned them a bit as they came up and ended up with tons of cherry tomato plants that produced like crazy. We are in zone 5 (northern Indiana), I don't know if that makes a difference. That is the only experience I know of, but I am a bit of a newbie at this.

I always seem to get volunteer cucurbits out of the compost. This year they were watermelon. I've had tomatoes and winter squash in the past.

I had brussels sprouts live 2 years in this climate. Because of the drought they hadn't produced sprouts but since they seemed to be growing I left them all summer.

I planned on picking them last fall for Thanksgiving dinner. We had a warm spell, something hatched out caterpillars, and I lost every last sprout. :-(

So its possible to leave some ripe tomatoes on the ground where you want next years tomatoes to grow? How about leaving your some of your potatoes in the ground? Onions to get seeds? Anything else?

You don't mention where in the UP you are. There is a big difference in the weather conditions depending on if you are on the garden pennslulya or along lake superior.

You may be able to over winter onions, plant some NOW to get them established. Use some this fall for green onions and let the rest go. If the weather is good to you you will have some early green onions in spring. These will quickly go to seed so you will have to use them by early June. In fact I have 3 year old onions growing in my old veggie garden, I am turning this into a perennial flower bed so I just left the onions there and get big pink/white flower heads every july that looks like part of the flower garden.

You could leave some tomatoes (fruit not plants) on the ground and hope they sprout in spring. Every year I get volunteer toms growing, usually cherry or pear varieties. The plants will not overwinter in our zone.

I am a little farther south than you, but I have had late-planted spinach over-winter in years we get good snow cover to insulate it.

Also you want to plant garlic in the fall to harvest next Aug. You can plant carrots now for a fall crop, and if you can keep the area well insulated you can harvest until the ground finally freezes.

As far as spuds, if you leave a few hills they may start go grow again in spring. Again I have some in the old veggie garden that have been there for 3 years, They are purple peruvian and not worth digging up IMHO, but have pretty purple leaves, so I leave them there for decoraton.

So much depends on the winter conditions in your area. I am in Central WI and will probably have a milder winter than you. The best thing to do is experiment and find out what works in you area.

Munising area along the Lake Superior shoreline. Snow belt! Plenty of cold and snow, sometimes early.

Well your tomatos are going to need a head start
I have very healthy volunteers but they don't even have fruit yet and the others have been turning red

tomatoes in the UP? forget it. My tomatoes in SE MI have not shown even the slightest pink. But there are many things that you can plant now for next year, all in the cool climate crops group.

1) hardneck garlic. plant in october for harvest in August.
1.5) if you do have garlic, save some bulbil heads and plant them now. In February you will have garlic shoots for omelets.
2) multiplier onions. Same as garlic.
3) arugula, corn salad and miner lettuce (all smallgreen plants) should be able to overwinter and produce some greens in March-April.

under cover:

4) The UP near the lake is not so cold when it comes to minimum temperatures. If you are willing to build one or more hoophouses, you can plant now Russian kale and harvest it through the winter. It is a bit late for radicchio, I have two beds planted for winter consumption (under cover).
5) also, if you had planted them earlier, carrots, parsnips for picking through the winter (under cover or under leaves, you can't pull them out when the ground is frozen). You might still be able to plant beets, same treatment as carrots.
6) also under cover, favas for greens. You may be able to plant them now, but then you will have to build the hoophouse. It is actually a couple of hours per hoophouse if you have everything ready.

You can also plant potatoes and sunchokes now for next year, if there are not many voles in your area.

I do have a small unheated greenhouse but have only used it to start seedlings.