You can try multiplying by a gain factor near unity at whatever you think is "near" 0 that scales rapidly to small values for range of input signal, filter, then inverse gain the result. That should leave more or less continuous.
Or, you can just try it and see if can live with discontinutiy by just selecting y(y<thresh) and operating on it.
I don't know of any specific work of the type but there well may be if look for it in literature.