Hi,
You can potentially create a custom field in the "product" table via the menu Display > Custom fields and display the text "out of stock" for the desired items but let an unlimited quantity to them.
Then you will have to create a plugin to divide the price of the current order by 2, and create another order with the rest of the amount. This way the customer will pay 50% directly, and another order is created, and he will be able to pay it via the user control panel once you set it a valid status.
Here is documentation for plugins:
hikashop.com/support/support/documentati...r-documentation.html