Log in with email but no password

You could use authenticate filter for that. Below you can see how it’s called:

$user = apply_filters('authenticate', null, $username, $password);

So if you write your own filter which will select user only based on login/username, then it should work (maybe some other minor tweaks would be necessary).

PS. But I don’t think you should do this. Authenticating users without passwords is rather big security problem. You also need to remember, that only some users should be authenticated this way (for example I’m pretty sure, that admin should still use password).