Sources close to Shelly tell us ... the reality star's family has received multiple phone calls from people threatening
violence ... even making threats against Shelly's 8-year-old daughter.
We're told Shelly's employer has also been receiving harassing phone calls -- demanding the company fire Shelly immediately because of the way she voted on the show.
Sources tell us Shelly's family is preparing to get the FBI involved -- because they're taking the threats VERY seriously.
UPDATE: "Big Brother" Executive Producer Allison Grodner released a statement on Twitter ... saying, "No matter how much you dislike an HG, this is wrong! True BB fans do not try to ruin lives. Please stop!"