How did Jame Gumb get to live in Mrs Lippman's House?

Question

In The Silence of the Lambs, the serial killer Jame Gumb is living in Mrs Lippman's house, where he keeps his victims, having murdered her (and, apparently, not even bothered to dispose of her body).

How did he come to take over her house? Wouldn't her relatives, seamstresses or the police paid a visit when she went missing?

Answer 1

In the novel The Silence of the Lambs which the movie is based on, in Chapter 59, where the author presents some background information about Jame Gumb

Reporters pieced together his history, beginning with the records of Sacramento County:
     [...]
     Years ago, when Dr. Lecter was declared insane, the therapy-session tapes had been turned over to the families of the victims to be destroyed. [...]. When the relatives called the lawyer Everett Yow and threatened to use the tapes in a renewed assault on Raspail’s will, Yow called Clarice Starling.
     The tapes include the final session, when Lecter killed Raspail. More important, they reveal how much Raspail told Lecter about Jame Gumb:
     Raspail told Dr. Lecter that Gumb was obsessed with moths, that he had flayed people in the past, that he had killed Klaus, that he had a job with the Mr. Hide leather-goods company in Calumet City, but was taking money from an old lady in Belvedere, Ohio, who had made linings for Mr. Hide, Inc. One day Gumb would take everything the old lady had, Raspail predicted.
     “When Lecter read that the first victim was from Belvedere and she was flayed, he knew who was doing it,” Crawford told Starling as they listened together to the tape. “He’d have given you Gumb and looked like a genius if Chilton had stayed out of it.”
     “He hinted to me by writing in the file that the sites were too random,” Starling said. “And in Memphis he asked me if I sew. What did he want to happen?”
     “He wanted to amuse himself,” Crawford said. “He’s been amusing himself for a long, long time.”
     No tape of Jame Gumb was ever found, and his activities in the years after Raspail’s death were established piecemeal through business correspondence, gas receipts, interviews with boutique owners.
     When Mrs. Lippman died on a trip to Florida with Gumb, he inherited everything—the old building with its living quarters and empty storefront and vast basement, and a comfortable amount of money. He stopped working for Mr. Hide, but maintained an apartment in Calumet City for a while, and used the business address to receive packages in the John Grant name.

Answer 2

The script has additional information that Gumb took over the house when it was supposed that Ms Lippman moved to Florida and died there two years previously.

Clarice is talking to one of Fredrica Bimmel's (the first victim) friends, Stacy..who tells her that Mrs. Lippman died.

         She died. She went to Florida to 
         retire, like two years ago? She died 
         down there.

This line is omitted from the movie though...but there is dialogue in the movie which covers the same ground.

Clarice: I'm looking for Mrs. Lippman's family.

Gumb: No. The Lippmans don't live here anymore.

[Omitted]...Conversation about why Clarice is there and whether he knew Frederica

Gumb: Mrs. Lippman had a son. Maybe he could help you. I got his card in here someplace. Do you want to come in while I look for it?

[More omitted]...

Clarice: Did you take over this place after Mrs. Lippman died? Is that right?

Gumb: Yeah. I bought this house two years ago.

So it's apparent that there was nothing suspicious about Mrs. Lippman's disappearance (assuming it was in fact her in the tub, and we don't know that it is).

Everyone thought she'd gone to Florida to retire.