International law never allows such killing of unarmed people trying to cross a country's border.
Are there any international laws, processes or rules to return dead body in these circumstances?
From wikipedia:
Felani Khatun a 15-year-old Bangladeshi girl, was shot and killed by India's Border Security Force (BSF) on 7 January 2011, at the India-Bangladesh border. A photograph showing Felani Khatun's dead body hanging on a border fence made of barbed wire was picked up by international media...
The question starts with a wrong statement, that international law does not allow the use of force against unarmed border violators. It does. There are human rights involved, and any one border policy may be against international law and conventions, but generally speaking the use of (lethal) force may be allowed.
When a person dies, the proper disposition of the body is governed by the laws of the country where the body rests. This can become problematic when the body rests on a border fence, possibly inaccessible from the side on whose territory it is. Once the body is recovered, there may or may not be an autopsy, again according to national law.
I would imagine that the grieving family would have to make visits to their country's foreign affairs ministry as well as the nation holding the body's embassy or consulate (Embassy is generally the HQ of a diplomatic mission and are in a host nation's capital in a nation while consulates are satellite offices that allow for more local access to general services, which this arrangement would likely be. The number of consulates will vary depending on the size of the nation and the demand for services. I know many nations with close relations to the U.S. will normally maintain several consulate in addition to Embassy due to the size and population spread of the U.S.).
In the event that the two nations do not have formal diplomatic relations (an example like the U.S. and Iran, which severed times after the Iranian Hostage Crisis in the 70s) you may need to look for your nation's Protecting Power with respect to the other nation. In diplomacy, the protecting power is a nation that both nations do have diplomatic relations with and will work on the protected power's behalf if needed. (In the U.S.-Iran situation, the U.S. asked and was accepted by Switzerland to be their protecting power in Iran. Note that protecting powers are typically one way channels as the other nation may designate their own nation to be their protecting power. In this situation, while the Swiss may protect American interests in Iran, Pakistan protects Iranain interests in the U.S.).
