There was a nearby ship when the Titanic was sinking, but the crew was asleep.

Barely had it set sail on its maiden voyage than the ship that was hailed as ‘unsinkable’ sank, with at least 1,517 lives lost (some say it’s more), and it turned out to be one of the deadliest maritime calamities ever.
The sinking of the Titanic led to safety regulations being bolstered in a bid to make ships safer, and some of the provisions include sufficient lifeboats to carry all on board, as well as having ships staff their radios around the clock.

The SS Californian is described as the ‘Ship Who Watched Titanic Sink’. When the Titanic was sending out distress signals, officers aboard the Californian saw several rockets and tried to alert their captain, Capt. Lord. However, he had since gone to bed. No effort was made to wake the wireless operator and it was assumed the rocket signals were company signals of some kind. There were officers aboard the Californian who believed there was something serious happening though.
As the Titanic appeared to be leaving the area full of icebergs following eight white rockets to alert anyone in the vicinity, this was reported to Captain Lord but he preferred to do nothing. This, notwithstanding the fact that the two ships were just a few miles apart. The Californian itself was sunk during World War I and the wreckage has never been found. Call it a twist of fate.