The census takers often would write the information into their notebooks, and then fill in the forms later. Sometimes they were careless and didn't transcribe it correctly, or couldn't read their own writing. I think that's why we see some ridiculously wrong ages sometimes.

I bet he wrote something like "Elinr" or "Elin A" in his notebook and scrawled the last bit, so he then wrote it into the form as "Eliza". I'm just guessing, of course.

For this reason, we have to stretch our imaginations a lot when we can't find somebody in the census. I found her by searching for the daughter Elizabeth.