In which country did the Jews think they were going to stay when they left Sighet?

For the most part, the Jews of Sighet are in denial over the fate that awaits them. They've heard first-hand testimony from Moshe the beadle about the brutal treatment meted out to their co-religionists in Budapest, but the general consensus is that the Nazis's activities will be limited to Hungary's capital city and will not extend to a small, remote town like Sighet.
However, the Nazis do come to Sighet and soon occupied the town and begin the process of preparing the town's Jews for their looming deportation. Even after the Jews are gradually stripped of their rights and herded into a cramped ghetto, many still cling to the stubborn delusion that all will be well. The Jews are given some measure of control over their own lives in the shape of a Jewish Council, but it's all just a ruse by the Nazis to lull their prisoners into a false sense of security.
When the time comes for the ghetto to be liquidated, no one really knows what will happen next. The Jews of Sighet know they're going to be transported, but they have no idea where. Eliezer's father tells him there are rumors that the Jews will be sent to work in brick factories in Hungary, where they will be well away from the front. However, the rumors are false, and Eliezer, his family, and the other Jews of Sighet are to be transported to the notorious Auschwitz death-camp in Poland.