From the api polygon documentation :
You can also create a polygon with holes by passing an array of latlngs arrays, with the first latlngs array representing the outer ring, while the rest are holes inside.
So, I think you can use this to make a really big polygon for the outer ring, and the province is cut out like a hole inside. Of course, if you zoom in to a level larger than the large polygon, it will be inconvenient. It might be best to set a minimum scale to prevent this from happening.
var polygon = L.polygon( [[[52, -1], [52, 1], [50, 1], [50, -1]],
Jsfiddle
Or set an external polygon to cover the whole world:
[[90, -180], [90, 180], [-90, 180], [-90, -180]]
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