They should put in writing a set of guidelines as to what the new employee can and cannot do with respect to information from the old employer. If the employee violates any of those guidelines, it could result in termination or the withdrawal of any indemnification promise.
For example, the employer could say, "We are hiring you and want to make sure you are not bringing with you confidential information, that you have not copied or downloaded anything, that you have not kept copies at home, that you have not contacted any of your former customers until we do so in coordinated manner, and if for any reason we find out you have done any of the above, you could be disciplined up to immediate termination."
What about tacit knowledge, the information in employees' heads? Could an employee get sued over that?
The law treats tacit knowledge just like it was knowledge on a piece of paper. There are clear, established guidelines as to what is acceptable and unacceptable behavior on the employee's part in what is called the Uniform Trade Secrets Act that courts in California have adopted, and which I think has been adopted in 40 states. Even with those guidelines, it's hard for employees to follow those rules, particularly if they're in sales because that's how they make their money.
What you can do is send out an announcement about your new job that has all your contact information, but it can't be a solicitation. Just a tombstone announcement: 'So-and-so has gone to work at X and here's the phone number.' Then you sit back and wait for the phone to ring. If customers call you, you are free to talk to them and you will be protected under the law.