Cell phone signal boosters are required by the FCC to have the ability to auto-detect oscillation, and to take corrective action when it is detected[1]. When oscillation is detected, the signal booster will automatically reduce its gain, or signal boosting power, in an attempt to correct the condition[1]. If the reduced gain does not correct the oscillation condition, then the booster must shut itself off[1]. This happens within a few hundredths of a second[1].
Brands known for cell phone signal boosters include Cel-Fi, HiBoost, SureCall, and weBoost[4]. HiBoost signal boosters have smart software that guarantees overall network protection, and are enabled with automatic gain control (AGC)[7]. AGC optimizes the booster's performance according to the outside signal strength, and if the signal is too strong, the power of signal amplification automatically decreases[7]. This avoids interference and prevents the booster from overload[7]. HiBoost boosters also have self-oscillation detection, and will automatically detect the problem and reduce gain to fix it if the booster and antenna are too close to each other[7]. The HiBoost Hi23 EDW also has self-oscillation protection to ensure that it operates smoothly without interference[5].
Citations:[1] https://www.weboost.com/blog/antenna-separation-and-why-its-important
[2] https://www.waveform.com/a/b/guides/best-signal-boosters
[3] https://www.signalbooster.com/blogs/news/prevent-oscillation-or-feedback-in-signal-booster-installations
[4] https://www.pcmag.com/picks/best-cell-phone-signal-boosters
[5] https://mobilesignalbooster.pk/shop/hiboost-hi23-edw-mobile-signal-booster/
[6] https://www.ubersignal.com/blogs/articles/get-the-most-out-of-your-weboost-signal-booster
[7] https://eu.hiboost.com/product/hi17-5s/
[8] https://www.wilsonpro.com/blog/commercial-cell-phone-signal-booster-oscillation-and-overload
[9] https://powerfulsignal.com/support/knowledgebase/consideration/what-is-cell-signal-booster-oscillation/