"All the 47 interviewees that we managed to locate ... were not asked to provide phone numbers or addresses to the Israeli authorities, and, of course, they had no contact with the Israeli authorities after they left," Rozen said.
The majority of Eritreans plan to smuggle their way into Ethiopia and try to survive there, while some head on the dangerous route through Sudan and Libya for Italy, with the hope of finding refuge in Europe.
"We receive a lot of calls and emails from worried relatives around the world - and also in Israel - about people who left and disappeared," Rozen said.
Captured by ISIL
Aman said five Eritreans aboard his flight out of Israel tried to make it to Europe but were captured and killed by the Islamic State of Iraq and the Levant group in Libya. He pulled out his phone and played an online video by ISIL
, known as ISIS - showing preparations for beheadings - and identified two people he knew being led to their deaths.
While Aman did not fall into ISIL's hands, he faced significant danger and uncertainty. Similar to Mesgen's story, Aman said when he landed in Kigali he was sent to a nearby hotel and two days later was smuggled out of Rwanda to Uganda.
From there, he tried to reach South Sudan, but was caught by border guards who did not let him leave until he surrendered all the money he had left from the $3,500 that Israeli authorities handed him when he left. They let him keep $50 and told him to go away.
"I didn't have clothes, I didn't have a bag, nothing," Aman said.
His younger brother was in Israel at the time, but now also lives in Germany. He sent Aman some money to Juba, capital of South Sudan. After collecting the cash, Aman travelled to Khartoum, Sudan's capital, where he met his wife who he had not seen in six years.
She is an Eritrean who had been living in a refugee camp in Ethiopia. The couple made their way through Libya - where they again were captured and forced to pay ransom - and then across the Mediterranean Sea on an overcrowded smugglers' boat with hundreds of other people from various countries.
No data is available on how many asylum seekers who left Israel voluntarily made it to Europe. However, it is well documented that more than 10,000 people died in the Mediterranean Sea over the past three years trying to reach its shores.
The lucky ones
Aman and his wife arrived in Germany in October 2014. He said the journey from Rwanda to Germany cost $11,000, which was spent on official bribes and smuggler payments.
Mesgen - who was aboard a smuggling boat that was lost at sea for 48 hours before being rescued by the Italian navy - managed to reach Germany in September 2015. He said he paid $10,000 for a similar trip.
Both men were eager to tell their stories because they know many Eritreans still in Israel and wanted to raise awareness about the consequences of the voluntary departure programme. Aman and Mesgen emphasised how fortunate they were to survive.
There are 29,367 Eritreans still in Israel, according to the latest data published by the Israeli Immigration and Population Authority. As of last December, there were 1,860 Eritreans and Sudanese living in the Holot Detention Centre for Illegal Immigrants, the Israeli newspaper Haaretz reported.
In Germany, Aman's and Mesgen's asylum applications were reviewed within months, and they were granted refugee status with all its social and economic rights.
Throughout the EU, about 93 percent
of Eritrean asylum applicants are granted some form of protection.
Aman and Mesgen are currently full-time students at a state-funded language school, and both recently became fathers for the first time. Aman and his family live in the centre of Berlin, while Mesgen, his wife - also an Eritrean refugee - and toddler have a two-room flat on the southern outskirts of the German capital.
The rent for both their apartments is covered by Germany's welfare system, and each family gets a monthly allowance of about 1,000 euros ($1,050).
"I am happy to be here," Mesgen said recently outside a Berlin church that serves a community of Eritrean refugees every Sunday morning. "Here it is good, thank God. I'm lucky."