"No...don't take her, I beg you..." Where you were dying after fighting Gyutaro along with Tanjiro, and Uzui and you were the one in the worst situation.

When Sanemi heard the news about how precarious you were in a situation, he didn't hesitate to run to where you were and try to help.

You can survive with Nezuko healing you or if you want to be dramatic (like me) it can make you in such a deplorable situation that there was no longer any salvation!! >w<