Ah seeing your edits.

So the question about magnetic strength limits given zero resistance is very interesting! Glad to see interest as it's an obvious question very few people ask.

All superconductors have a property we call critical field. Above this limit the material is no longer able to compensate for and exclude magnetic fields, and the superconducting properties collapse.

So if we made a coil of say YBCO (a common type 2 in lab examples) and we pumped more and more current through it, eventually it overwhelmed the material and suddenly resistance would skyrocket, generating heat causing a feedback cycle and it would probably melt to slag.