Softened adverbs are provided in this article. The words listed here are commonly found along with the verb softened in sentences. This reference page helps answer the question what are some adverbs that describe or modify the verb SOFTENED.
completely, considerably, easily
finally, gradually, greatly
immediately, instantly, previously
quickly, slightly, slowly
suddenly, sufficiently, thoroughly
usually
Hope this word list had the softened adverb you were looking for. In addition to adverbs used with softened, other example verb adverb pairings can be found on this site.
You can help by adding more adverbs in the comments. Thanks.