Unprotected cells won’t stop instantly, but unprotected LiIon’s do need to be monitored as to discharge voltage level. There’s no real consensus on how low the limit should be, but 2.8V to 3.0V is generally optimum, with about 2.5V being about as low as they should ever see.
Most of us use awareness of the light output or a runtime found through actual use to know when we’re nearing our preferred limits with unprotected cells so we can swap them out or recharge them. In this usage it is critical to not have the light suddenly stop so I would chose unprotected and become familiar with them. Needing to replace an over-discharged cell is a far better option than suffering the damages of a crash or a damaged bike and over-discharging in use is not unsafe; those problems arise after use during charging.
Read LiIon Safety 101 if you haven’t yet done so, then buy only quality cells which folks here on BLF recommend as added protection against problems, as well as getting value for your money. Unprotected cells are safe when used properly, they just require paying more attention to their discharge level. It’s not hard to do and it also saves some money since they’re cheaper to buy.
Phil