Amy, one of this year's original Islanders, has been criticised by some viewers over her actions towards Lucie Donlan.
This week saw Lucie face elimination alongside her then-partner Joe Garratt, who was the one voted out.
The pair were put up for the axe by a number of the other Islanders, including Amy, who had to vote for the least compatible couple.
In a response to the hate sent to Amy's social media accounts, her family posted a statement this week titled simply: "Be kind, always 💕"
They wrote: "We would like to thank those who continue to support Amy and those who have sent kind messages through this whole Love Island experience, but especially over the last few trying days.
"Everyone is entitled to their own opinion, however the way some people are gunning for Amy is shocking and really upsetting for her friends and family and everyone who knows and loves her.
"The other couples also voted for Lucie and Joe as least compatible due to their recent ups and downs, and nobody in the villa knew it would end in any islanders being voted out."
The post continued: "The volume of hateful comments and death threats we have received over the last couple days has been completely off the scale and extremely upsetting. They still continue to come through, and it stems from one comment made four episodes ago which was said in support of Lucie.
"Amy is a fierce friend. She is kind, loyal and supportive. She wants the best for everyone and is willing to give herself entirely to those she cares about.
"Amy is not malicious or vindictive and she is certainly not a bully.
"We would like to ask those sending malicious and vile messages to think about the implications of their words and threats before plastering them over social media."
They concluded: "Anyone who knows Amy knows she does not deserve this."
Love Island 2019 continues nightly on ITV2.