The "destitute" are the class of homeless who are beyond helping themselves. They can be found in nearly every nation.
Some have not taken a shower in years. They are even destitute of friends. They are no longer able to care for themselves. They own nothing. Some are reprobate. Others are broken in health or worn down by old age. Some are broken mentally. Some are simple minded while others have learning disabilities.
The destitute are unable to help themselves, therefore it is society's responsibility to care for them.
To let them wander around in a destitute condition is sinful. You may not have the ability to do much for them personally, but you could take their case to the government. The government needs to be made aware of their responsibility to the destitute.
"Blessed [is] he that considereth the poor: the LORD will deliver him in time of trouble." Seriously consider what can be done for the poor; and do what is in your power for them. "Open your mouth, judge righteously, and plead the cause of the poor and needy." You can start at city hall.
That which you do for the least of them, you do for the Lord of glory himself. The very measurement of your love for the Lord is what you are doing for the poor and needy.