diff --git a/CHANGELOG.md b/CHANGELOG.md
index b7b0398864..a3b06bdaef 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -12,6 +12,7 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 - IPython now respects when a `Console` instance is passed to `pretty.install` https://github.com/Textualize/rich/pull/3915
 - Fixed extraneous blank line on non-interactive disabled `Progress` https://github.com/Textualize/rich/pull/3905
 - Fixed extra padding on first cell in columns https://github.com/Textualize/rich/pull/3935
+- Fixed trailing whitespace removed when soft_wrap=True https://github.com/Textualize/rich/pull/3937
 
 ### Added
 
@@ -33,7 +34,7 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 
 ### Fixed
 
-- Fixed exception when callling `inspect` on objects with unusual `__qualname__` attribute https://github.com/Textualize/rich/pull/3894
+- Fixed exception when calling `inspect` on objects with unusual `__qualname__` attribute https://github.com/Textualize/rich/pull/3894
 
 ## [14.1.0] - 2025-06-25
 
diff --git a/rich/text.py b/rich/text.py
index b5b114b42e..60109dd9e8 100644
--- a/rich/text.py
+++ b/rich/text.py
@@ -691,7 +691,6 @@ def __rich_console__(
     ) -> Iterable[Segment]:
         tab_size: int = console.tab_size if self.tab_size is None else self.tab_size
         justify = self.justify or options.justify or DEFAULT_JUSTIFY
-
         overflow = self.overflow or options.overflow or DEFAULT_OVERFLOW
 
         lines = self.wrap(
@@ -1232,12 +1231,15 @@ def wrap(
             if "\t" in line:
                 line.expand_tabs(tab_size)
             if no_wrap:
+                if overflow == "ignore":
+                    lines.append(line)
+                    continue
                 new_lines = Lines([line])
             else:
                 offsets = divide_line(str(line), width, fold=wrap_overflow == "fold")
                 new_lines = line.divide(offsets)
-            for line in new_lines:
-                line.rstrip_end(width)
+                for line in new_lines:
+                    line.rstrip_end(width)
             if wrap_justify:
                 new_lines.justify(
                     console, width, justify=wrap_justify, overflow=wrap_overflow
diff --git a/tests/test_text.py b/tests/test_text.py
index 93a98d7c0a..b528608ad7 100644
--- a/tests/test_text.py
+++ b/tests/test_text.py
@@ -1092,3 +1092,21 @@ def test_append_loop_regression() -> None:
     b = Text("two", "blue")
     b.append_text(b)
     assert b.plain == "twotwo"
+
+
+def test_soft_wrap() -> None:
+    """Regression test for https://github.com/Textualize/rich/issues/3841
+
+    Soft wrap should not strip trailing whitespace.
+
+    """
+    console = Console(color_system="standard", width=80, force_terminal=True)
+    text = Text(" Hello World ", style="white on blue")
+
+    with console.capture() as capture:
+        console.print(text, soft_wrap=True)
+
+    output = capture.get()
+    print(repr(output))
+    expected = "\x1b[37;44m Hello World \x1b[0m\n"
+    assert output == expected