In British English you have the word, layabout, a person who habitually does little or no work. It comes from the idea of someone who lacks the energy or will to even stand and do any chores, preferring to spend their days between lying in bed or on the sofa.
A layabout is usually referred to unemployed people who are uninterested in finding a job; lazy teenagers; and husbands who do nothing in the house all day.
She regretted ever asking that layabout to be her roommate, as he
created the mess of two people and refused to help with anything
In answer to the question title
Is there a word for someone who has others do all their work for
this is trickier. The question implies that this person is idle, lazy and in the fortunate position of having more than one person available to perform these duties or jobs. The word, boss, a tongue-in-cheek solution which was suggested in the comment section, doesn't quite fit. Although a boss may delegate duties and give orders, this doesn't exclude the employer from being hardworking and conscientious him/herself.
The OP is looking for the equivalent of slave master or slaveholder, a person who owns a group of people who are deprived of the right to leave, are forced to obey and perform any job or work the slaveholder sees fit, without pay. To this day slaveholders still exist, in 2005, the International Labour Organization provided an estimate of 12.3 million forced labourers in the world and
A report by the Walk Free Foundation in 2013, found India had the
highest number of slaves, nearly 14 million, followed by China (2.9
million), Pakistan (2.1 million)
So either expression may be used very effectively and both are, logically, derogatory terms.
A more figurative equivalent of slave master/slaveholder would be slave driver, someone who makes people work very hard, in other words a demanding, unyielding taskmaster.
The new boss is a real slave driver