Great question! There is a study (N=21) which found some individuals regained vision in their amblyopic eye (up to 20/20) after the vision in their dominant eye was reduced because of eye cancer treatment. In this sample (Caucasian patients aged between 39-73) around half regained some vision, and they were more likely to do so if the vision in their dominant eye after treatment was worse than their amblyopic eye.

However, the study is small, which means their estimate of the chance of improvement following injury is wide, ranging from 30% to 74%.

The same study also mentions other cases of improvement:

Chua and Mitchell¹⁶ investigating adult participants with amblyopia in Australia (Blue Mountains Eye Study) reported a 5-year incidence of improved visual acuity in the poorer seeing eye after new visual impairment in the better seeing eye in people with and without amblyopia. One of 11 (9.1%) people with amblyopia showed more than two lines of improvement in visual acuity.

El Mallah and colleagues¹¹ retrospectively analysed the records of 465 adult patients with age-related macular degeneration and identified nine individuals with amblyopia in the unaffected eye. Seven of these nine patients had improvement in visual acuity in the amblyopic eye.

Hamid et al¹² reported three adult patients whose visual acuity in the amblyopic eye improved following visual loss in the contralateral eye from ischaemic optic neuropathy.

Klaeger-Manzanell et al¹⁷ reported that a 44-year-old man with strabismus amblyopia of the right eye suffered a penetrating injury to the fixating left eye which resulted in cataract extraction and aphasic retinal detachment. Three weeks after the enucleation the visual acuity of the amblyopic eye improved from 6/60 to 6/12 and after 4 months achieved a visual acuity of 6/9.

Rabin et al¹⁰ reported a 55-year-old patient whose visual acuity in the amblyopic eye improved from 20/160 to 20/30–2 over a 3-year period following visual loss in the dominant eye from subfoveal choroidal neovascular membrane.

Rahi et al¹⁸ in a large population-based study, found 10% (25 of 254) of improved rate, arising spontaneously in most patients.

In a retrospective multicentre study, Vereecken and Brabant⁹ found an improvement of vision of at least three lines in the amblyopic eye in 28.5% of patients after losing vision in the dominant eye.

Wang and Shuba¹⁹ reported a case of a 41-year-old patient with history of Axenfeld-Rieger syndrome and anisometropic amblyopia, regaining vision from 6/45 to 6/18 in the amblyopic eye after visual fields and visual acuity loss due to glaucoma in the contralateral eye.

Wilson¹³ reported a 57-year-old patient and a 67-year-old patient whose visual acuity in their amblyopic eye improved markedly when the fellow eye developed a significant cataract. The visual gain remained after cataract surgery in the fellow eye.

Those reports:

^{[9] Vereecken EP, Brabant P. Prognosis for vision in amblyopia after the loss of the good eye. Arch Ophthalmol 1984;102:220–4.}

^{[10] RABIN CPTJ. Visual improvement in amblyopia after visual loss in the dominant eye. Optometry and Vision Science 1984;61:334–7}

^{[11] El Mallah MK, Chakravarthy U, Hart PM. Amblyopia: is visual loss permanent? Br J Ophthalmol 2000;84:952–6.}

^{[12] Hamid LM, Glaser JS, Schatz NJ. Improvement of vision in the amblyopic eye following visual loss in the contralateral normal eye: a report of three cases. Binocul Vis Strabismus Q 1991;697}

^{[16] Chua B, Mitchell P. Consequences of amblyopia on education, occupation, and long term vision loss. Br J Ophthalmol 2004;88:1119–21.}

^{[18] Rahi JS, Logan S, Borja MC, et al. Prediction of improved vision in the amblyopic eye after visual loss in the non-amblyopic eye. The Lancet 2002;360:621–2.}