The only practical way to repair this is to remove the pan and pull it out from the bottom.
Don't push it down any more. It it gets loose in the pan it could cause a lot of damage.
If you leave it and just plug the dip stick hole so oil doesn't come out, it won't hurt anything. But you won't be able to check the oil either.
If you don't have any oil leaks and it doesn't burn an excessive amount of oil, the amount of oil usage should be fairly predictable. Just set your trip meter and put in a quart every 2,000 miles or so.
Then when you have to do some significant repair that requires the pan to be removed, do it then.
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First off, I'm sorry I took so long to answer your question. Jobs alway get in the way of life.
There's no guarantees that the dispstick isn't going to continue to drop and get wound up in the crank case.
It depends a lot on how much dispstick is left in the hole. If it broke off at or very near the handle, there would be a long piece in the hole and it would be pretty stable. If the piece in the hole is shorter, there is a greater chance that it would come lose and cause damage.
I got the impression from your first question that the dipstick broke at the handle. That would be the best place for it to break. The dipstick can only drop about an inch or so because it will hit the bottom of the pan. Since it's not flexible, it should stay in place.
I thought of another option last night. I don't recall how much of a tube is sticking out of the block. If there is enough tube that you can stick a rod or screwdriver down the hole and feel the end of the dipstick and the end is within that tube, you would have a couple of choices.
Bandaid fix would be to take a vice grip and crush the tub onto the dipstick.
The better fix would be to pull the dipstick tube out of the block along with the dipstick and replace both.
Is there any way you could send me a picture of the tube with a screwdriver in the hole resting on the end of the remaining dipstick?
I'm glad your trip went well and nothing happened. That had to be a bit stressful.
I expect the dipstick is still in the tube, but it depends on where it broke off.