LOS ANGELES (CNN) -- The hunt for the man who sprayed a California family with bullets -- killing two and wounding three -- continued Sunday, as the mystery behind the shooting deepened.

Late Saturday night, police said they discovered a body in suspect Desmond John Moses' charred Inglewood home.

The body has not been identified.

Police believe Moses set the home, a rental, on fire early Saturday before allegedly making his way to the front of the property -- to the home of Filimon Lamas.

There, hidden behind a painter's mask, Moses opened fire on the family: Lamas, the 28-year-old mother and their four kids, police said.

Lamas threw his body over the kids to shield them from the bullets.

He died.

His 4-year-old son was shot in the head.

Although the children's mother was maimed by gunshot wounds to both legs, she mustered the strength to run from the house carrying the boy. But he, too, later died.

A 6-year-old son, shot in the pelvis, and a 7-year-old daughter, wounded in the chest,were both in critical but stable condition.

The mother also was in critical but stable condition Saturday.

The only one to escape unhurt was Lamas' oldest child, an 8-year-old boy.

Police did not release names of the mother or any of the children, pending notification of relatives.

As firefighters searched through the rubble of Moses' home, a manhunt ensued for the 55-year-old unemployed welder whom police described as a "hoarder" in his rental home.

"What would motivate an individual to do this is inexplicable," Inglewood Police Chief Mark Fronterotta said.

CNN's Maria P. White contributed to this report.

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