Hi there,
I’m not a designer, but I take care of the newsletters for a small cinema I’m volunteering for. I had the idea to place a piece of text inside a black 1px border on an almost white background, because I just think it looks cool and strong. But: are black borders appropiate only for funeral advertisements? I looked for this on the internet but couldn’t find anything!
I hope professional designers can help me with my question 
Borders, like any other design element, should only be used if they contribute something to the design intent. Doesn’t matter if it’s a funeral notice or a birthday invitation.
Borders of any type are apt to be miss-cut in some fashion. If you use a one-point border, keep it well in from the trim edge, as in inside the safety.
Even then, your white space outside the border is apt to be slightly off.
Thank you for your reply.
The piece of text I wanted to put in the border is sort of extra information. It should be clear that it’s different from the main text.
And my possibilties are limited. One of the options is to place a bordered text field, and you can change the thickness, color and style 
If a black border around a box does what you want it to do, then use it. Without seeing what you have in mind, I can’t offer an opinion on it, but black borders are commonplace for all kinds of purposes.
Thanks!