It is known that Dobby was the house-elf (servant) which belonged to the Malfoy family; until he was set free by Lucius (as set-up by Harry with a sock in Tom Riddle's diary) in Harry Potter and the Chamber of Secrets.
What is interesting is that there is no mention of the Malfoys replacing Dobby (that I know of), even considering:
- How upset Lucius was to lose Dobby:
Lucius Malfoy stood frozen, staring at the elf. Then he lunged at Harry.
“You’ve lost me my servant, boy!”
But Dobby shouted, “You shall not harm Harry Potter!”
There was a loud bang, and Mr. Malfoy was thrown backward.
-Harry Potter and the Chamber of Secrets, Chapter Eighteen (Dobby's Reward).
- It is customary for "old families"1 to have house-elf servants, and given that the Malfoy family are one of the oldest (and wealthiest) families2, you would think that they would acquire a new house-elf.
1. House-Elf Wikia Page
2. Malfoy Family Wikia Page