Princella Ross, 65, was found unresponsive inside the home on Beran Drive after a caregiver arrived to check on her, according to police and family members.
First responders initially were called around 9:30 a.m. for what was believed to be a medical emergency. The Houston Police Department said it later determined Ross had been shot.
Sgt. Charles Lamont said investigators believe the shooting happened roughly nine or 10 hours before Ross was discovered. No 911 call was received around the time of the shooting.
"It looks like a safe neighborhood, but residents say they hear gunshots all the time," Lamont said. "That's why there was no 911 call."
A family member, who declined to be identified because of safety concerns, said Ross initially believed a hole in her left arm was related to her diabetes or insulin. Police later determined it was a bullet wound.
Family members said Ross was a mother of three and grandmother of 10.
Her daughter described the loss as devastating.
"Empty. Loss. I don't know how to feel. I'm pissed off," she said.
Police said investigators are searching the neighborhood for surveillance video and other evidence. No arrests have been announced.
Investigators have not determined whether Ross was the intended target. Police said her home was the only one on the block struck by gunfire overnight.
Anyone with information about the shooting or the people responsible is urged to contact Houston police.