A starter motor takes the power it needs to turn the load. If the battery voltage is low, the current increases. In a DC circuit power is the product of voltage and current. The high current likely welded the starter relay contacts closed.
Yup! I had this happen once in my old S-10 Pickup in front of the liquor store. It cranked and cranked but never started and got everything hot enough that it actually melted a big hole in the battery where the terminal was mounted. I was trying to twist the battery cable loose to pry it off but couldn't.
That was around 20 years ago and ever since that I never have my battery cables so tight that I can't loosen them quickly with no tools in such an emergency.
Came in handy again just last month when my soon-to-be ex-wife was drunk as hell and trying to drive off in my van, but that is another story!