There are few wide-open spaces in quarian spacecrafts; liveships are the exception. Each ship is a massive hydroponics facility, growing thousands of tons of genetically modified staple crops under artificial light and in highly enriched soil.
The surface of a liveship is studded with docking bays so as many shuttles as possible can distribute the foods throughout the flotilla on a daily basis. When received, the crops are sterilized with radiation, ground up into nutritious pastes, and pumped into quarian suits through feeding tubes. In return, waste products that could be used as fertilizer or compost are returned to the liveships through an efficient (if odorous) recycling program.
Liveships do not hold animals. The quarians consume a vegan diet, driven not by ethics but by practicality. Captive animals require living space, and consume large amounts of water and plant matter. The quarians cannot afford such an inefficient resource-to-calorie ratio, to say nothing of the live animal's disease or allergen potential. As a result, when the flotilla arrives in a star system where live is based on the same dextro-amino acids that the quarians consume, pastes based on animal proteins fetch highly inflated prices, and the vendors are typically mobbed by quarians wanting a new taste sensation. The sickness that often follows these binges is treated much the same way as hangovers are in human culture; painful, but part of the overall experience of excess.