Might be worthwhile to note that share owners must trust DividendRippler (not the asset) for BTC, LTC, as well as TRC.
But what exactly happens if you don't? Will Ripple find a trading path to your account so you receive it in some other currency?
No alternative payment is attempted at this point. You might trust DR for BTC and not LTC but the best order in the market might be below your expectation.
What happens is simple, the payment stays failed until you retry it, and will fail again if you retry it without granting proper trust. Also, there is one global retry per day, so just add the trust line and within 24hrs at most the payment will be sent.