Those are two separate issues. You want austenite because it is ductile and has get damage tolerance.
Elements that are Aus stabilizers also include N, C, and Cu.
Balancing these alloys is tricky, each element has solubility limits and also can have impact on properties ranging from strength to welding.
Commercial 18/8 alloys (304 or 316) are not very stable. Slight amounts of cold work will trigger martensite formation (note the magnetism).
Carbide formation is detrimental because it takes Cr out of the alloy and that lowers corrosion resistance. This is the worst right around the carbides. This local depletion is why you get intergranular corrosion (IGA) in grain boundaries (the carbides will form in the grain boundaries first).
There are SS grades with other structures, Ferritic (FeCr with very low C), Martensitic (basically high Cr steels), and Duplex (mixed Aus/Fer). Each has its own properties and reasons for use.
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P.E. Metallurgy, consulting work welcomed