Cockroaches can indeed infest outdoor spaces such as yards if conditions are favourable. They are attracted to food sources like organic debris, compost, and waste, as well as water sources and sheltered, moist areas. Warmth and outdoor lighting can also attract them. To minimize the risk of an outdoor infestation, it’s advisable to keep the yard clean, fix leaks, avoid over-watering, seal outdoor trash and compost bins, and maintain a clear area free of dense vegetation and debris around the building's foundation.