We know very little about Burns (more about her sister, who lived much longer than she did), but enough to suggest she had a substantial impact on the evolution of Engels's thinking. Perhaps most importantly, it was very likely she who acted as his guide, and guaranteed his safe passage, through the Manchester slums, an experience he turned into his first and in many ways defining book, The Condition of the Working Class in England.

Engels diagnosed her death as the product of "heart disease or stroke" – there was no autopsy and no doctor attended, so that is likely as close to the truth as we will get. She had been a heavy drinker at this point for many years.

I summarised what is known, and can reasonably be deduced, about the rest of her life in an essay about Burns which you may find useful:

Friedrich Engels' Irish Muse.