In academia, one is forced to read papers that come out.
Not in academia. You are not forced to read anything at all after you get your PhD. As a graduate student, you may have regular reading assignments given by your adviser, but those are just like any other class assignments, so I don't think you are talking of them here.
Some of the papers I read are directly related to my work and then it is reasonable to read them in my working hours. Others are completely irrelevant and I read them just for the pleasure and to broaden my knowledge in other areas. These, I think, should be read in one's free time.
One funny thing in academia (if we are talking about academia and not about an industrial job that pretends to be one) is that you never know what exactly your work is. Any time a colleague may stop by and ask a question, a paper may come for refereeing, etc., which may give you an opportunity (not "force", because you can reject anything you don't want either bluntly or in some fancy way like "Interesting problem but, unfortunately, it is outside my area of expertise") to think of something you've never heard of before. Another funny thing is that there is no work time (except teaching and meeting hours) and free time. You can wake up at 2AM and work like crazy if you have a good idea, or you can lock your office and go for a long stroll in the town if you don't feel like sitting and bumping your head against the brick wall will result in anything any time soon. I read whatever I want and wherever and whenever I want, and suggest that you do the same, provided that you meet your obligations and do not go on reckless reading (or non-reading) sprees.
But then there are papers that are not directly related to what I am doing but may turn useful for my work, e.g., they may use a method that might come handy although they deal with a slightly different field.
Zillions of them! No chance to read them all, of course, but, by all means, look out and around whenever you have a chance.
Should I read such papers at work as well or should I read them in my free time?
Whichever you prefer. I like reading when lying on a sofa and I don't have one in my office, so I read everything at home. Some people prefer to clearly separate the work and the social life, so they do all their reading at the office. There are no rules and no obligations in this respect.
How do I decide where the border between work-related and leisure-read papers lies?
Currently there is no such border in academia. We enjoy the total absence of the "reading police" and the internet made everything (well, almost: the copyright still spreads its shadowy tentacles far and wide but they are cut out one by one every day) available at a click of a button. The real danger is not in the "legal issues" but in the effective management of your time, which is the reverse sign of the freedom coin. But that is a totally different story...