Emma Watson, 32, was discovered in the Wishaw property on November 10.
A couple of days' earlier she had disappeared from the property, in the Gowkthrapple area, but was later traced by police.
There are no suspicious circumstances surrounding her death.
Relatives launched a crowdfunder to raise money for her children to 'make sure these kids get exactly what they deserve for Christmas'.
A statement on the page read: "Emma Watson our beautiful angel sadly left our lives on Sunday, November 10.
"Behind she leaves her wonderful family but most important her four amazing young kids; Ella, Mirren, Olivia and Lomond.
"Just a few weeks before Santa comes they have lost their beautiful mummy and we would like to make sure these kids get exactly what they deserve for Christmas.
"Emma had the biggest heart and would give to anyone even if it was her last.
"Let's give her the send off she deserves and ensure her kids can make happy memories."
More than £1000 has already been gathered.
To donate, visit the Just Giving page.