Constable Lesley Harrison, 29, accepted the risk of violence as part of her work, her brother said.
In the attack on Sunday night she was stabbed three times - one wound punctured her heart - when she attended a reported burglary with a woman colleague.
Police said a 28-year-old man from Liverpool, who was treated for a head wound, was in custody in connection with the incident.
PC Harrison, of Warrington, Cheshire, was in intensive care last night at the Royal Liverpool Hospital. The assistant chief constable (operations) of Merseyside, Paul Acres, said she was 'very seriously ill'.
PC Harrison was stabbed in the left arm and chest and is understood to have lost two pints of blood. In her five years on the force, she has been beaten up in a street attack, hit on the head by a brick and suffered a dislocated shoulder chasing a burglar - forcing her to take almost 12 months off work.
Her brother Brian Harrison, 27, said: 'She has been hurt before but that didn't bother her. She looked on it as part and parcel of a job that she was being paid to do.'
PC Harrison was attacked close to the spot where she was beaten up a year ago. She said after that attack: 'Some officers go through their whole service without a single injury. I am just unlucky.'Reuse content