This character is a Nonspacing Mark and inherits its script property from the preceding character. The character is also known as long slash overlay.
The glyph is not a composition. Its width in East Asian texts is determined by its context. It can be displayed wide or narrow. In bidirectional text it acts as Nonspacing Mark. When changing direction it is not mirrored. U+0338 prohibits a line break before it. The glyph can be confused with 18 other glyphs.
The Wikipedia has the following information about this codepoint:
A bar or stroke is a modification consisting of a line drawn through a grapheme. It may be used as a diacritic to derive new letters from old ones, or simply as an addition to make a grapheme more distinct from others. It can take the form of a vertical bar, slash, or crossbar.
A stroke is sometimes drawn through the numerals 7 (horizontal overbar) and 0 (overstruck foreslash), to make them more distinguishable from the number 1 and the letter O, respectively. (In some typefaces, one or other or both of these characters are designed in these styles; they are not produced by overstrike or by combining diacritic. The normal way in most of Europe to write the number seven is with a bar. )
In medieval English scribal abbreviations, a stroke or bar was used to indicate abbreviation. For example, ⟨£⟩, the pound sign, is a stylised form of the letter ⟨Ꝉ⟩ (the letter ⟨L⟩ with a cross bar).
For the specific usages of various letters with bars and strokes, see their individual articles.