You are right to identify that in Chapter Seven, Jonas is left alone in his group of peers as the only one who has not received an assignment. If you look at the end of the chapter, this is something that clearly makes him very uncomfortable and also causes him to consider what he has done wrong:
He hunched his shoulders and tried to make himself smaller in the seat. He wanted to disappear, to fade away, not to exist. He didn't dare to turn and find his parents in the crowd. He couldn't bear to see their faces darkened with shame.
However, as Chapter Eight begins, we see that this feeling of shame and isolation ends and is replaced by something infinitely better, as we discover that Jonas has been singled out for a unique job that only one other person in the community has: the Receiver of the community. The Receiver of Memory is not assigned, as the Chief Elder says, but "selected." The difference between this job and others is explained by the Chief Elder:
"But the Receiver-in-training cannot be observed, cannot be modified. This is stated quite clearly in the rules. He is to be alone, apart, while he is prepared by the current Receiver for the job which is the most honoured of our community."
So, Jonas has not been assigned because he has been selected to perform the most important job of the entire community. As he soon discovers, the normal rules do not apply to him, and he is given considerable leniency.