diff --git a/src/huggingface_hub/hf_file_system.py b/src/huggingface_hub/hf_file_system.py
index f19f8551aa..ea86537710 100644
--- a/src/huggingface_hub/hf_file_system.py
+++ b/src/huggingface_hub/hf_file_system.py
@@ -4,7 +4,7 @@
 import tempfile
 from dataclasses import dataclass
 from datetime import datetime
-from typing import Any, Dict, List, Optional, Tuple, Union
+from typing import Any, Dict, List, NoReturn, Optional, Tuple, Union
 from urllib.parse import quote, unquote
 
 import fsspec
@@ -180,7 +180,7 @@ def _align_revision_in_path_with_revision(
                 revision = _align_revision_in_path_with_revision(revision_in_path, revision)
                 repo_and_revision_exist, err = self._repo_and_revision_exist(repo_type, repo_id, revision)
                 if not repo_and_revision_exist:
-                    raise FileNotFoundError(path) from err
+                    _raise_file_not_found(path, err)
             else:
                 repo_id_with_namespace = "/".join(path.split("/")[:2])
                 path_in_repo_with_namespace = "/".join(path.split("/")[2:])
@@ -195,9 +195,9 @@ def _align_revision_in_path_with_revision(
                         path_in_repo = path_in_repo_without_namespace
                         repo_and_revision_exist, _ = self._repo_and_revision_exist(repo_type, repo_id, revision)
                         if not repo_and_revision_exist:
-                            raise FileNotFoundError(path) from err
+                            _raise_file_not_found(path, err)
                     else:
-                        raise FileNotFoundError(path) from err
+                        _raise_file_not_found(path, err)
         else:
             repo_id = path
             path_in_repo = ""
@@ -229,7 +229,7 @@ def _open(
         revision: Optional[str] = None,
         **kwargs,
     ) -> "HfFileSystemFile":
-        if mode == "ab":
+        if "a" in mode:
             raise NotImplementedError("Appending to remote files is not yet supported.")
         return HfFileSystemFile(self, path, mode=mode, revision=revision, **kwargs)
 
@@ -413,7 +413,21 @@ class HfFileSystemFile(fsspec.spec.AbstractBufferedFile):
     def __init__(self, fs: HfFileSystem, path: str, revision: Optional[str] = None, **kwargs):
         super().__init__(fs, path, **kwargs)
         self.fs: HfFileSystem
-        self.resolved_path = fs.resolve_path(path, revision=revision)
+
+        mode = kwargs.get("mode", "r")
+        try:
+            self.resolved_path = fs.resolve_path(path, revision=revision)
+        except FileNotFoundError as e:
+            if "w" in mode:
+                raise FileNotFoundError(
+                    f"{e}.\nMake sure the repository and revision exist before writing data."
+                ) from e
+
+    def __del__(self):
+        if not hasattr(self, "resolved_path"):
+            # Means that the constructor failed. Nothing to do.
+            return
+        return super().__del__()
 
     def _fetch_range(self, start: int, end: int) -> bytes:
         headers = {
@@ -462,3 +476,14 @@ def safe_revision(revision: str) -> str:
 
 def safe_quote(s: str) -> str:
     return quote(s, safe="")
+
+
+def _raise_file_not_found(path: str, err: Optional[Exception]) -> NoReturn:
+    msg = path
+    if isinstance(err, RepositoryNotFoundError):
+        msg = f"{path} (repository not found)"
+    elif isinstance(err, RevisionNotFoundError):
+        msg = f"{path} (revision not found)"
+    elif isinstance(err, HFValidationError):
+        msg = f"{path} (invalid repository id)"
+    raise FileNotFoundError(msg) from err
diff --git a/src/huggingface_hub/lfs.py b/src/huggingface_hub/lfs.py
index 1aad3250e5..e6c1b7f276 100644
--- a/src/huggingface_hub/lfs.py
+++ b/src/huggingface_hub/lfs.py
@@ -422,6 +422,7 @@ def _upload_parts_hf_transfer(
             progress.update(total)
         return output
 
+
 class SliceFileObj(AbstractContextManager):
     """
     Utility context manager to read a *slice* of a seekable file-like object as a seekable, file-like object.