JSF will not permit the entry of invalid data. That's one of its core concepts. And there is no number that corresponds to "".
If you use the Integer data type instead of "int", then setting it to null might work, but I won't guarantee it. I don't know what the spec says is supposed to happen and I'm too lazy to RTFM.
The only way I can guarantee that an empty value will be accepted is if you define the property as a
String. However you would then need a validator to prevent non-numeric data from being set in the backing bean.
The secret of how to be miserable is to constantly expect things are going to happen the way that they are "supposed" to happen.
You can have faith, which carries the understanding that you may be disappointed. Then there's being a willfully-blind idiot, which virtually guarantees it.