command.CommandText = "SELECT * FROM [Question] WHERE [Test_Id] = @test_id";
command.Parameters.Add("@test_id", DbType.Int32).Value = test.Id;
var reader = command.ExecuteReader();

//...

var buffer = new byte[IMAGE_FIELD_SIZE];
Image image;
using (var stream = new MemoryStream())
{
  long bytesRead;
  while ((bytesRead = reader.GetBytes(reader.GetOrdinal("Image"), 0L, buffer, 0, buffer.Length)) > 0) // Исключение выпадает здесь
  {
    var actualRead = new byte[bytesRead];
    Buffer.BlockCopy(buffer, 0, actualRead, 0, (int) bytesRead);
    stream.Write(actualRead, 0, actualRead.Length);
  }
  image = ByteArrayToImage(stream.ToArray());
}

CREATE TABLE [Question] (
  [Id] INTEGER PRIMARY KEY AUTOINCREMENT,
  [Text] NVARCHAR(500) NOT NULL,
  [Image] BLOB NULL DEFAULT NULL,
  [Test_Id] INTEGER NOT NULL,
  CONSTRAINT [FK_Question_to_Test] FOREIGN KEY ([Test_Id]) REFERENCES [Test] ([Id])
);

в System.Data.SQLite.SQLiteDataReader.VerifyType(Int32 i, DbType typ)
в System.Data.SQLite.SQLiteDataReader.GetBytes(Int32 i, Int64 fieldOffset, Byte[] buffer, Int32 bufferoffset, Int32 length)

Image image;
try
{
  var buffer = new byte[IMAGE_FIELD_SIZE];
  reader.GetBytes(reader.GetOrdinal("Image"), 0L, buffer, 0, buffer.Length);
  image = ByteArrayToImage(buffer);
}
catch (InvalidCastException)
{
  image = null;
}
catch (InvalidOperationException)
{
  image = null;
}