In my mom's case, she had a co-worker accidentally step on her toe. It became infected and just wouldn't heal. She tried treating it herself at home for a long time, instead of going to the doctor and it developed gangrene. When she did go, she was put in the hospital for IV antibiotic coverage and wound care. Her circulation was compromised, causing it not to heal. She went in for surgery, hoping just to lose a toe, but the circulation was so impaired that they removed her foot. That wound didn't heal, so they ended up amputating her leg above the knee, as that was where they found the best blood flow.
She was 47 or 48 when she lost her leg, but she'd been a T2 diabetic for 20 years by that time, and was very non-compliant. She was first started on insulin while in the hospital with her toe. My grandfather also lost his leg to a non-healing ulcer, but that was in the 70's.
I've mentioned to my internist my concerns about circulation and what happened to mom and grandad. He told me it's very rare anymore for anyone to have to have an amputation if they seek medical attention at the first sign of an infection.