Yes. A cyclist could be at fault in a bicycle accident if their actions breached their duty of care to themselves and other road users. For instance, failing to yield, riding against traffic, and failing to use their designated lanes can make a cyclist liable for their accident.
You should note that cyclists can share liability in a bicycle accident, especially if their actions don’t entirely contribute to the accident. In this case, the pure-comparative negligence principle applies. In this principle, the cyclist will only recover damages worth the percentage fault of the driver in causing the accident.