Answer by taking a quote from the following article:

Joseph Carey Merrick (5 August 1862 - 11 April 1890), often incorrectly called John Merrick, was an English man with very severe face and body deformities who was first exhibited at a freak show as the "Elephant Man", and then went to live at the London Hospital after he met Frederick Treves, subsequently becoming well known in London society. Merrick was born in Leicester, and began to develop abnormally during the first few years of his life: his skin appeared thick and lumpy, he developed enlarged lips, a bony lump grew on his forehead, one of his arms and both of his feet became enlarged and at some point during his childhood he fell and damaged his hip, resulting in permanent lameness. When he was 9, his mother died from bronchopneumonia, and his father soon remarried. Merrick left school at the age of 13 and had difficulty finding employment.

Merrick left school aged 13, which was usual for the time. His home-life was now "a perfect misery", and neither his father nor his stepmother demonstrated affection towards him. He ran away "two or three" times, but was brought back by his father each time. At 13, he found work rolling cigars in a factory, but after three years, his right hand deformity had worsened and he no longer had the dexterity required for the job. Now unemployed, he spent his days wandering the streets, looking for work and avoiding his stepmother's taunts.  Merrick was becoming a greater financial burden on his family, and eventually his father secured him a hawker's licence which enabled him to earn money selling items from the haberdashery shop, door to door. This endeavour was unsuccessful, since Merrick's facial deformities rendered his speech increasingly unintelligible and prospective customers reacted with horror to his physical appearance. Housewives refused to open doors for him and now people not only stared at him but began to follow him out of curiosity. Merrick failed to make enough money as a hawker to support himself. On returning home one day in 1877, he was severely beaten by his father and he left home for good.  Merrick was now homeless on the streets of Leicester. His uncle, a barber named Charles Merrick, heard of his nephew's situation, sought him out and offered him accommodation in his home. Merrick continued to hawk around Leicester for the next two years but his efforts to earn a living met with little more success than before. Eventually, his disfigurement drew such negative attention from members of the public that the Commissioners for Hackney Carriages withdrew his licence when it came up for renewal. With young children to provide for, Charles could no longer afford to support his nephew. In late December 1879, now 17 years old, Merrick entered the Leicester Union Workhouse.  Merrick became one of 1,180 residents in the workhouse. Joseph was given a classification to determine his place of accommodation. The class system determined which department or ward he would reside as well as the amounts of food he would receive. Joseph was classed as class one for able bodied males and females. On 22 March 1880, only 12 weeks after entering, Merrick signed himself out of the workhouse and spent two days looking for work. With no more success than before, he found himself with no option but to return to the workhouse. This time he stayed for four years. Around 1882, Merrick underwent surgery on his face. The protrusion from his mouth had grown to 8-9 inches and severely inhibited his speech and made it difficult to eat. He was operated on in the Workhouse Infirmary under the direction of Dr Clement Frederick Bryan and had a large part of the mass removed.

Did he work there long?
after three years, his right hand deformity had worsened and he no longer had the dexterity required for the job.