Can you "draw to" anything but a close?
Solution 1:
To draw to a head — TFD
(Med.) To begin to suppurate; to ripen, as a boil.
To ripen, to approach the time for action; as, the plot draws to a head
I found this from Google Ngrams. I get draw to a close, conclusion, head, point, crisis, certain, scale, period, plea. Most of those do not appear to be idiomatic, or they do not work the same way as "draw to a close" does.
