This is somewhat arcane, but important world. Understanding these rules can sometimes prevent a case from being valid on a technicality. While it is likely that if a plaintiff's attorney wants to serve you he can, it is also true that through procrastination or error, many times the effort occurs late or is flawed.

Filing Within the Statute of Limitations
While the deadline is usually fixed, the plaintiff's attorney may claim the deadline should be extended due to some piece of information he requested not being available, or other circumstances. But exceptions are unusual.
If you are concerned a suit may be filed, check with the courthouse in your likely counties. This includes where you have offices, where the patient involved may live, and where any hospital involved may be
Both attorneys and process servers do make mistakes, and more so if they are at the deadline. If you are aware that the process is near a statue of limitations deadline, a few days of careful attention to how it occurs can make the difference in whether a case is valid. And such instances are not uncommon.

First the case is filed. This must occur within the statute of limitations. Often this is 2.5 years from the completion of care regarding the clinical problem at issue. While this may be a matter of uncertainty or argument for your attorney to look into, also be aware it may be extended. Reasons for longer statues of limitations include a minor under 18,
a mentally incapacitated patient, or a foreign object left in at surgery.
 
Once filed, you can learn of that at the courthouse, as mentioned above. But it needs to be served within a further deadline, often 120 days. Also the judge can extend this deadline at times.
If you learn a case is filed but not served, you of course need to notify your insurance carrier. You may also want to discuss the issue of how serving occurs with your key office staff and family. This allows you to keep the matter more discreet. And also you do not want your employees or family to inadvertently turn an improper or late service into a valid one, by failure to understand the process.
 
Serving a Filed Case:
The service has to meet certain criteria, and these aim at serving to you, or a responsible adult representing you who understands what the papers are when accepting them.
They can serve you at your business, or perhaps with the state because your business is registered with the state and has a presence there, legally.
They can serve the papers at your home. This is usually done by a process server. You will want to check local rules, but usually they will go to the front door, or some exposed door that appears to be a routine entrance. They are not supposed to go to other doors, enter on their own, or go around the yard. If the first few efforts fail, the criteria in some localities is three, they can leave the papers at the door and then mail it to you as well, this is called nail and mail.

If you are close to the deadline then a delay in accepting it may be worthwhile, as it will go over the filing deadline. Improper service, giving it to wrong party and leaving, or a party not responsible for the process can make the case invalid.
As mentioned, there can be ways around a serving deadline, on occasion. Your attorney can speak to this based on local rules.