Monica Jean Gallagher was the estranged wife of Frank and the mother of Fiona, Lip, Ian, Debbie, Carl, and Liam.
Monica left her family prior to the series starting, something that all the Gallagher children resent her for to some degree (Fiona and Lip especially). At the time the kids were 9 (Fiona), 1 5 (Lip), & 3 (Ian).
Although Monica wasn’t exactly a good person, it is showed that she always means well for her family. Due to her bipolar disorder and her addiction to drugs and alcohol, she is often unable to control herself, but at least tries to do what she thinks will benefit the Gallaghers.
After one final return in Season 7, it is revealed that she has Brain damage. Her death is shown in Happily Ever After when Frankis trying to wake her up, unsuccessfully.
After dying, she passed on 70000$ worth of methamphetamine to her family, one final attempt at fixing the broken bond between her and them.