Yes it is a responsibility of the community because if someone cannot afford legal services and they are really innocent in the crime they are putting the wrong person in jail. It is the communities responsibility to get the real person that committed the crime of the street not just put away someone that cannot afford a lawyer.
As a matter of justice and fair play which is the entire idea of the courts and legal system, the poor should have a legal defense just as a rich person does. The court system and legal system can never be considered fair and just if the poor are lacking legal defense.
No, legal services for the poor are not a responsibility of the community beyond defense at trial, because people are often in legal situations because of their own doing, so it stands to reason that it should be their own job to find a way to navigate the legal system. The community also could not afford to provide a lawyer for anyone who needs it.
Legal sources for the poor, beyond defense at trial, are not the responsibility of the community. As the Supreme Court has construed it, the Sixth Amendment of the U.S. Constitution requires that the defendant be provided with counsel in the event that the defendant cannot secure legal counsel by him- or herself. This is already a substantial burden upon the administrative resources of the judicial system. To ask yet more of a community, especially when such services are not enjoined by the Constitution, is to ask too much; the resultant strain would very likely result in the diminution in quality of those services already on offer.
The poor should be responsible for all of the things that they do, this includes any court proceedings followed by any acts they committed. The same way they committed these acts, the same way they can better theirs lives and find a way to get any services they need after.