Solution that automatically scales to dimensions of an element would be usage of CSS3 linear-gradient connected with calc() as shown below. (There were some issues with Chrome in times of v30+ versions that this answer originally described but looks like they got resolved in the meantime and in v90+ it works as expected).
.crossed {
background:
linear-gradient(to top left,
rgba(0,0,0,0) 0%,
rgba(0,0,0,0) calc(50% - 0.8px),
rgba(0,0,0,1) 50%,
rgba(0,0,0,0) calc(50% + 0.8px),
rgba(0,0,0,0) 100%),
linear-gradient(to top right,
rgba(0,0,0,0) 0%,
rgba(0,0,0,0) calc(50% - 0.8px),
rgba(0,0,0,1) 50%,
rgba(0,0,0,0) calc(50% + 0.8px),
rgba(0,0,0,0) 100%);
}
<textarea class="crossed"></textarea>