Most samurai belong to the order of the warrior and are dedicated to their lord. Those without a lord, or who chose to abandon their lord, are ronin. A samurai may instead elect to dedicate himself to one of the orders listed under the cavalier description, but such samurai are rare.
A samurai who wishes to change his order must undertake a lengthy process to dedicate himself to a new cause. When this choice is made, he immediately loses all of the benefits from his old order. He must then follow the edicts of his new order for one entire level without gaining any benefits from that order. Once he has accomplished this, he gains all the bonuses from his new order. The only exception to this is when a samurai decides to become a ronin. A samurai can elect to become a ronin immediately, losing all the benefits from his old Classes order and replacing them with the new benefits from the ronin order. Once a ronin, however, the only way for the samurai to change to another order is through the method described above. Note that the names of these orders might vary depending upon the campaign setting or GM’s preference.
That's really all that is said about it.
Basically, the closest thing I can find is that you would become a ronin. Alternatively, it seems reasonable that if your lord has an successor that you could go and pledge your loyalty to them and maintain your current order.
Historically, that liege who died of natural causes had a son who assumed the same title and responsibilities and the samurai just served that new liege. New oaths were made and life went on as before (except for the dead liege, of course).
Some didn't want to; they chose to become ronin rather than serve the new guy, usually for personal reasons (such as not liking or more probably, not respecting, the kid who just took over).
If the old guy had no heir, then ronin was the only option.
Regardless of reason, most ronin would find some lord somewhere in the next town down the road and join up so they could have a home and a job and a duty. Not all - some stayed ronin either by choice or by dishonor, but most just basically found a new "job" with a new lord.