Many of us have had that problem. We're searching for an ancestor and finding him or her in census records, vital records and more.
Just when we think we're on a roll, that ancestor disappears! That's when you need to expand your search to other records such as orphanages, workhouses or almshouse (poorhouse) records.
Here's a few resources for such records (but there are many more both online and offline)
New York Almshouse Records 1819-1840 - These contain the names of the ship each person sailed on, plus dates of arrival.
New York Almshouse Records 1855-1858 - These contain the name of the ship and the arrival date and port for each person.
Poor Law Union Immigrants to Canada 1836-1853 - Lists of individuals from various parishes in England sent to Canada when their Parish could no longer support them
Passenger List of Waegh (The Weigh-House), 1655 - with names and ages of the Almshouse children, who sailed to New Netherland (New York) from Amsterdam Holland
Orphan Records New York Lists of children in Orphanages from 1850 - 1880
List of Poor sent from England to Ireland 1860-1862 -Includes Ports of Departure & Arrival plus number of years in England or Scotland