The same group is thought to be behind at least five break-ins at the homes of elderly residents in the Oldbury, Wednesbury, Smethwick and West Bromwich areas.
Each incident has involved threats of violence and cash and jewellery being stolen - including one incident where a woman in her 90s had her father's war medals stolen on Remembrance weekend.
At this stage, detectives do not believe the death of a 78-year-old man in Halesowen is connected to the break-ins.
Officers are now urging people to check on their elderly neighbours and have stepped up patrols in a bid to identify and catch the group.
Timeline of break-ins:
Saturday, November 13, Oldbury: Masked men smash back door of 94-year-old woman's home and steal war medals and jewellery at around 7pm
Sunday, November 14, Smethwick: Three men, one armed with a crowbar, make threats and steal cash
Monday, November 15, Wednesbury: Burglars strike in the morning
Monday-Tuesday, November 15-16, Wednesbury: Burglars strike overnight in same town
Tuesday, November 16, West Bromwich: Handbag stolen in latest linked break-in
Chief Inspector Keeley Bevington from Sandwell Police said: “It appears these offenders are deliberately targeting the homes of older residents. It’s really despicable and we’re determined to catch whoever is behind these burglaries.
“Enquiries are underway: we’ve carried out forensic examinations, taken statements and are examining CCTV.
“We know how upsetting these offences are for the victims, family, friends and the wider community.
“Please take time to talk to older neighbours and relatives about their security and things they need to do to stay safe.
"Pop round to check they’re OK, keep an eye out for any suspicious activity near their homes, and call us if anything seems amiss.”
One of the break-ins linked to the group saw a 94-year-old woman targeted.
The woman was left heartbroken and "very shaken" after her home in Hilltop Road, Oldbury, was broken into at about last week and her father's First World War medals were stolen.
Three men broke into the house made off with her rings plus the medals belonging to her late father, Thomas Morris, who received three bravery medals, including a Victory Medal engraved with ‘TA MORRIS’ on the back and attached to a rainbow ribbon.
The elderly woman was threatened and demanded to hand over her gold wedding band, engagement ring, an eternity ring with zirconia stones around the centre and another gold ring with a fish-like pattern
The incident was described as "despicable" by police at the time.
Anyone with information is urged to call 101 or Crimestoppers anonymously on 0800 555111.