Question: Can part of a state secede from the rest of the state?
For example, can Michigan secede from (Detroit) Wayne County? Pennsylvania from Philadelphia?
they would probably be better off.
Sure, and it's happened more than once, along with boundary changes.
Maine split from Massachusetts, Vermont "seceded" from New York, New Hampshire and/or Connecticut, take your pick, and of course, West Virginia from Virginia.
The U.S. Constitution is copasetic with all such changes provided, provided, provided they are done by mutual consent, meaning both States plus the U.S. Congress.
Makes sense?