When a constituent told Boston City Councilor Tito Jackson that an elderly resident had sold her home because she was repeatedly fined for failing to shovel her sidewalk during last winter’s relentless snowstorms, the story struck a chord.

“She was 80 and sold her house for under the market rate [because of the snow],’’ said Jackson. “We want our elders to be able to stay in the city of Boston. We want them to age in place, in their own homes for as long as possible. We know that they are the fabric of our community.’’

That’s why on Wednesday, Jackson will propose an ordinance that would exempt any Boston resident older than 60 from shoveling the sidewalks surrounding their property after a storm. The ordinance would also exempt people with disabilities.

Jackson is seeking a council hearing on the proposal.

Boston requires homeowners to remove snow from their sidewalks within three hours after a snowfall, or three hours after sunrise if it snows overnight, according to rules posted on the city’s website. Failure to do so can lead to a $50 fine.

During the nightmare of last winter, the city issued thousands of violations to shoveling scofflaws. By February, at least 4,000 such tickets had been issued since the first blizzard had hit. Unshoveled snow forced many pedestrians into the streets.

Jackson said the city sends mixed messages to its older residents, who make up an estimated 15 percent of the population, when it comes to snow removal. On the city website, elderly homeowners are encouraged to skip shoveling to avoid health complications. But at the same time, fines are doled out if they don’t comply with city rules, he said.

“Many [elderly residents] are on fixed incomes, so a fine can mean making very difficult decisions between vital needs. That is why I put this ordinance forward,’’ Jackson said.

Jackson said that ideally young people would be hired through the city to shovel for residents who meet the requirements of the proposed ordinance.

“We have a huge need for youth jobs,’’ he said.

Residents older than 60 would need to register with the city to qualify for the exemption.

Many people are still physically fit at 60. Jackson indicated that the age limit wasn’t set in stone.

“We will figure that out during the hearing,’’ he said in a follow-up statement. “Many cities have chosen different ages.’’

Jackson said the city would work with the Elderly Commission to spread information about the new rule, if it passes, and to aid elderly residents in the registration process.

“We have many elders who still own their homes and we want to make sure we are able to keep them in our homes in our communities,’’ Jackson said.

Steve Annear can be reached at steve.annear@globe.com. Follow him on Twitter @steveannear.