Yes.
It's not quite as rare as one or two posters above seem to imagine.
And (contrary to some of the opinions expressed above) not illegal at all, unless they fill their own trade before yours - that would be "front-running", which is illegal in some countries.
It's because of the facility to do this that some counterparty market-maker "brokers", especially of spot forex, keep some regularly winning clients on their books, because (as you rightly suspected when you asked the original question) it can be an additional profit-source for them, regarding the accounts of clients they've known well enough and for long enough.
Not in countries with proper regulation.
Which is another reason (as if anyone needed one) to avoid "brokers" regulated in places like Cyprus, Russia and Mauritius, whose reasons for choosing to be regulated in those countries are typically not ones in their clients' interests.
However, as also mentioned above (and in this case rightly), this isn't something that's in any way relevant to 99% of traders. My guess is actually 99.9%.