This feature is unique to your needs and therefore not likely to be available in the form you require it to be in. The main problem here is that we don’t know the capabilities of the remote database (does it have an API?) so at this point we have to assume there is no option for remote access.
This situation would be greatly simplified if the employer provided email addresses to the employees (.(JavaScript must be enabled to view this email address).) Do you remember how Facebook worked when it was restricted to college students? You had to sign up with an email address from the college before you could get access. You would then receive your access details.
You could do the same thing here. I think we could safely assume the employer has taken care of email access security, so we we could work from that. This would still require a custom add-on, but it would be more simple than the alternatives.
So, the process would work something like this…
The user signs up and the system checks the email address (pattern check to verify if the email address is part of X domain.) If there is a match on the domain, then the system allows the registration and sends an email with an auto-generated password to the user (who could then change the password.)
There are variations we could do, but you get the general idea.
ETA:
Just to be more clear, the user would only receive the password if that user can actually receive email at the address entered. This is like the reset email process. Anyone can initiate a password reset for any user (assuming that person knows the username the user signed up with) but only the person in control of that email address can finish the process.
BTW, if you would like to talk more about a possible add-on for this, then feel free to send me a PM.