So, you have a LInkedin account.  As with most users, many of your contacts are co-workers.  You leave your employer and send messages to your contacts on Linkedin.  Is that a problem?  It is a problem, if you have a non-compete with your former employer in which you agreed to not contact former your former co-workers.  That is what happened in one recent lawsuit.  The former employer, an IT staffing firm, learned of the messages and filed suit against the former co-workers.  See report.  

The former employee had signed a non-compete agreement in which he agreed to not solicit former co-workers.  So, sending an email to all his contacts, co-workers and others, which said, "Hey, let me know if you are still looking for opportunities," sounds like solicitation. 

So, yes, as the report explains, now, when an employee leaves a company, that employee may have to "un-friend" his/her former co-workers.  In this case, the non-compete clearly prohibited solicitation of former employees.