The casket is used by Rai for his hibernating periods. He had used it to sleep for 820 years when he went to hiding.
Most recently Rai uses it is after the fight with Rostere. He has to awaken both Tao and Takeo (due to their dying state as they couldn't be treated in the destroyed lab) which takes a heavy toll on his already deteriorated state. Frankenstein compels his master to enter a temporary hibernation in order to stabilize. Rai concurs and enters a short slumber in his casket. Frankenstein preserves the casket in a secured chamber within his house. When Frankenstein goes berserk during fighting the union elders, Rai awakens and leaves the casket just on time to save the ones under his protection.
The casket was supposed to be inside Rai's hiding chamber (the temple), but it had been placed in an abandoned flat by the time that he awoke from his long slumber.
It is later revealed that the casket had been stolen from a subsidiary branch of Union who had fished it out from the ocean bed. The group who stole it deals with ancient artifacts and they stole the casket to earn money. How it came to be in the ocean, however, is shown in the battle between Rai and Muzaka. Rai forms the casket on top of a ruined building in the middle of the sea on which he lands after leaping away from the fray, severely injured at his hip. Over a long period of time, the building was either worn away or knocked down, resulting in the casket sinking to the bottom of the sea. Frankenstein has remarked that everything is clear to him. In the OVA it is revealed that the casket was discovered by a scuba diver who works for the Union subsidiary.
As the casket was stolen from a Union subsidiary it didn't held much importance to Union and hence two low level agents, M-21 and M-24, were sent to investigate the whereabouts of this casket. In the process they met Rai and Frankenstein. Later, Mary and Jake came to supervise their investigation. The Union didn't know that Rai was in the casket.
Currently, the casket is being preserved by Frankenstein.