Furman was traded from the Giants to the Nationals in exchange for minor-league left-handed pitcher Tony Neubeck on Sunday, Jeff Passan of ESPN.com reports.
Lovelady was designated for assignment by the Nationals on Sunday, Kyle Williams of TheBanner.com reports.
Flaherty (forearm) was reinstated from the 15-day injured list Sunday and struck out one batter while allowing one hit and no walks over two scoreless innings in the Tigers' 4-2 loss to the Pirates in the season finale.
The Tigers optioned Hurter to the rookie-level Florida Complex League on Sunday.
Madden tossed three scoreless innings of relief with three strikeouts in Sunday's 4-2 loss to the Pirates.
Valencia went 1-for-4 with a solo home run in Sunday's 4-2 loss to the Pirates.
Ryan (0-1) took the loss against the Pirates on Sunday, allowing two runs on three hits and two walks with three strikeouts over 1.1 innings.
McGonigle went 2-for-3 with a solo home run in Sunday's 4-2 loss to the Pirates.
Tolman earned the save in Sunday's 6-4 win over the Mets, allowing a walk and one hit while striking out two over 1.1 innings.
Chaparro went 3-for-4 with a pair of solo home runs in Sunday's 6-4 win over the Mets.
