diff --git a/pdfplumber/page.py b/pdfplumber/page.py
index 096ee1b..96515db 100644
--- a/pdfplumber/page.py
+++ b/pdfplumber/page.py
@@ -13,6 +13,7 @@ from typing import (
     Union,
 )
 from unicodedata import normalize as normalize_unicode
+from warnings import warn
 
 from pdfminer.converter import PDFPageAggregator
 from pdfminer.layout import (
@@ -306,7 +307,12 @@ class Page(Container):
                     try:
                         extras[k] = v.decode("utf-8")
                     except UnicodeDecodeError:
-                        extras[k] = v.decode("utf-16")
+                        try:
+                            extras[k] = v.decode("utf-16")
+                        except UnicodeDecodeError:
+                            if not self.pdf.warn_unicode_error:
+                                raise
+                            warn(f"Could not decode {k} for annotation. {k} will be missing.")
 
             parsed = {
                 "page_number": self.page_number,
diff --git a/pdfplumber/pdf.py b/pdfplumber/pdf.py
index 9b6ea71..b00a6a2 100644
--- a/pdfplumber/pdf.py
+++ b/pdfplumber/pdf.py
@@ -35,6 +35,7 @@ class PDF(Container):
         password: Optional[str] = None,
         strict_metadata: bool = False,
         unicode_norm: Optional[Literal["NFC", "NFKC", "NFD", "NFKD"]] = None,
+        warn_unicode_error: bool = False,
     ):
         self.stream = stream
         self.stream_is_external = stream_is_external
@@ -43,6 +44,7 @@ class PDF(Container):
         self.laparams = None if laparams is None else LAParams(**laparams)
         self.password = password
         self.unicode_norm = unicode_norm
+        self.warn_unicode_error = warn_unicode_error
 
         self.doc = PDFDocument(PDFParser(stream), password=password or "")
         self.rsrcmgr = PDFResourceManager()
@@ -76,6 +78,7 @@ class PDF(Container):
         repair: bool = False,
         gs_path: Optional[Union[str, pathlib.Path]] = None,
         repair_setting: T_repair_setting = "default",
+        warn_unicode_error: bool = False,
     ) -> "PDF":
 
         stream: Union[BufferedReader, BytesIO]
@@ -107,6 +110,7 @@ class PDF(Container):
                 strict_metadata=strict_metadata,
                 unicode_norm=unicode_norm,
                 stream_is_external=stream_is_external,
+                warn_unicode_error=warn_unicode_error,
             )
 
         except PSException: