Do you have any wild plums nearby, or have you had a plum tree on a wild plum stock?
I have something similar coming up all over my garden, I took out a grafted Victoria plum tree last year which appears to be growing new plants off roots which run miles. For the last few years I have had these things growing further from the tree than you would think possible but I wondered if squirrels had planted plum seeds elsewhere. They are a nuisance, you can't get rid of them as they keep growing off seemingly forever living horizontal roots.
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