You can send any gcode even negative, that is not a problem.
If I understood your comment correctly you want this to be the new z=0, whcih you can do with
G92 Z0
Then firmware takes it as Z=0. Host will still show it as correct values since it adds the offset to output. Print will work none the less as expected.
Correct solution is of couse to adjust your zmin endstop to correct position. WIth zmax endstop you can simply increase zlength in eeprom.
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