Was I chosen to get bored and follow him and resign?
Do they have a reason to want you to resign? Did you show incompetence in your work at the company so far? Are you hated (for a valid reason or despite lack of it)?
Recruitment is an expensive process for companies and if they don't have a reason to want you out, they probably don't.
If you work in consulting, it might be that your company is pursuing an unethical but common strategy among consultancies - they tried to sell the client as many "resources" as possible and the client wasn't smart enough to understand your role isn't needed. So the client is paying for your "work", although you aren't doing anything. Your company is earning money and the only problem is you are bored. As I say, it's unethical, but not uncommon.
I've worked on large projects, where 20% of our consultants were such "placeholders". Their role was to pretend that they worked and were needed. The company was happy as they had 100% chargeability. Some of them even got promoted because of these roles! Of course, when you pretend to be working you can't snore or be missing since that's something the client would notice, even if they aren't the brightest. Which explains why your predecessor was fired.
Talk to your manager. Ask them whether they are happy with your performance. Ask them for more work. If they give a strange, avoidant explanation for your request for more work, it's probably because the explanation above (unethical behavior towards the client) is correct.
If the conversation doesn't bring anything you need to decide whether it makes sense for you to stay in a company in which you don't learn anything and basically waste time.