Can someone steal a check? Absolutely - check fraud of this variety is quite common. Sometimes people don't even need to forge a name or ID, because bank staff are human and don't always do their job as thoroughly as they are supposed to. Years ago a national TV program had a special where they went out and got banks to deposit - or even cash - checks made out to fictional characters like "Mick E. Mouse". There are also techniques like "check washing" where the document is physically altered, or just check printing where the information is taken off the check and placed onto a new document with a different "To" field.
However, in every single case - especially with government checks - everything remains quite traceable and the theft is usually quite temporary (at least to you). It is a hassle, but it is temporary and you can still get your money back without too much fuss.
First, contact the agency that issues your check and let them know you haven't received the check (which it seems you already did). Most agencies have a policy of waiting some period of days past the usual reception date before re-issuing or investigating a lost check, because the mail is not a guaranteed process. Due to the massive volume of mail and government checks sent out each month, checks are temporarily misrouted or mishandled as a part of natural error rates of the system, and many work themselves out over a week or two (letters get stuck in sacks, placed in the wrong bin, fall on the shop floor and get kicked under a desk, etc).
If you have reason to believe someone stole your check, you can let the agency know and request they re-issue the check (cancelling the old check) before the usual waiting period. They may or may not be willing to do this, and sometimes its a real hassle to get an agency to do this because it takes work and often some cost to do this and in the vast majority of cases the check wasn't actually stolen at all. If you urgently need the money for living expenses, many agencies have an "emergency re-issuance" policy they do not advertise, but you basically tell them you cannot afford to wait multiple weeks for a check due to some serious and pressing reason (you'll be evicted, you can't buy food, your utilities will be turned off), and request they re-issue the check immediately (or within a few days). I've had to do this before, and it's often annoying, but some agencies support this more readily than others.
Important note: if they re-issue the check and you end up receiving two checks, for the love of all that's holy do not deposit both checks! You'll be guilty of check fraud yourself, and even if you do it on accident it can cause a host of unwelcome issues.
In the future, if your agency supports direct deposit I would advise you to take advantage of it, as it eliminates checks and these kinds of annoyances often go away.
Finally, note that in most cases there is no risk to you if someone steals a government check intended to you, so long as you report the missing check in a reasonable period of time. If the check is cashed unlawfully the banks involved have whole divisions of people dedicated to handling these things and hunting down the money (and often the people involved themselves) to recover their own losses. This can take months or years, but in the mean time the banks (and sometimes government agencies) usually shoulder the loss until they can execute the recovery (or legal punishment).
From what you describe there is no upside to you to accuse anyone of anything based on scant evidence, so I would personally advise you not to cause yourself grief (or potential embarrassment/family discord) over a missing check. Just be aware that indeed this process can take days/weeks, so please plan your finances appropriately and if you will be put in urgent need make an emergency request of the check issuing agency.