When you build a minecart train using minecart furnaces and you have curves in your track, the whole train breaks. it doesn't matter if the passengers (e.g. rideable, chest, etc.) are being pushed or pulled by the minecart furnace, however the outcome will vary.
(see video, sorry for the bad quality...)
Minecarts with furnace are heavily broken (see MC-51053) and will be removed in a future version.