Lightning Network – In which case could I find funds stuck in a failed road?

The funds of the respective HTLCs remain blocked during a period of dead time if the payment_pre image do not spread along the road to your original channel. There is no guarantee that this spread will be successful. This is why HTLCs (sent) are always signed with a respective wait delay transaction, with a signed entry that uses this HTLC output in such a failure scenario.

Testing with smaller amounts that you offer ensures that only the lower amounts are captured in the HTLC exits of the commitment transactions in your channel, so that only a smaller amount would be "blocked" (this HTLC output is later usable by the respective wait time transaction during a channel closure). Thus, until the end of the waiting period, you have the remaining channel capacity with which you can carry out transactions.