励ます and 慰める: encouragement and consolation
Compare cheers that bolster a runner with comfort for someone in distress. Read the inability to find comforting words separately from an act of consolation or a recipient's recovery.
Who receives encouragement with 励ます?
励ます (はげます) means to encourage or bolster someone. In 「観客の声援が走者を励ます。」, the crowd's cheers encourage the runner; the sentence describes their function without reporting a finish or a race result.
「落ち込んだ友人を言葉で励ました。」 describes encouraging a dejected friend with words. Encouragement can address someone who is already discouraged, so 励ます is not restricted to support for an action that has yet to begin.
Comfort with 慰める and words that could not be found
慰める (なぐさめる) means to comfort or console someone in distress. 「母は失敗して落ち込む私を慰めてくれた。」 reports the mother's act of consoling the speaker, who was discouraged by failure.
In 「泣いている友達を慰める言葉が見つからなかった。」, the speaker could not find words to comfort a crying friend. 「慰める言葉」 identifies the kind of words being sought; it does not report that those words were found and used to console the friend.
The function of support and the recipient's condition
Cheering a runner and consoling someone discouraged by failure illustrate different functions of support. Words addressed to a dejected friend may serve both functions, so the recipient or the timing of an event does not create an absolute boundary between the verbs.
The inability to find comforting words tells us neither why the friend was crying nor whether the friend later calmed down. The mother's consolation is an actual act, but the sentence does not establish that the speaker fully recovered afterward.
Does the sentence about not finding comforting words tell us that the friend stopped crying?
Show the answer and why
No. 「言葉が見つからなかった」 says that words could not be found. The sentence does not report that comforting words were delivered or that the friend became calm.