For example, let's take Cross-Chain Swap on STON.fi (DEX on $TON on which HLTC will be implemented), to make DEX work fast and predictable, a timer is placed on each Swap, if one party fails to fulfill its obligations to the other, the funds of both parties are returned to their places. Thus a transaction cannot end with the loss of one party's funds.
How it works:
The parties to the transaction agree on a transaction time, generates hash values of secret pre-images, lock this and swap data into smart contracts on their blockchains, for example $TON and $BTC (user 1's hash is locked to user 2's contract).
Both parties verify the each other's contracts, and if one of the parties has the invalid contract - the swap canceled, funds refounded.
After the smart contracts are assembled, the parties disclose their secret pre-images, and the contract checks the hash of thems. If everything is correct - swap is done.